Multiscale Linear Transform

Purpose and expected result

Multiscale Linear Transform separates an image into detail layers plus a coarse residual, changes selected layers, and reconstructs the image. Use it for scale-selective detail suppression or enhancement, multiscale noise reduction, edge deringing, or residual-tone adjustment. It offers two undecimated models: configurable starlet smoothing (Starlet Transform) and Gaussian smoothings of the original image (Multiscale Linear Transform).

Apply is destructive: a successful run replaces the selected still or sequence. Optional deringing maps are separate views, and Preview snapshots are auxiliary images. Start on a duplicate. For calibrated linear data, keep strong stretching and range remapping disabled until the intended linear operations are verified.

At a glance

Item	Current behavior
Menu path	Process > Multiscale > Multiscale Linear Transform
Enabled when	An image or sequence is active. A launch is refused with a message when this process is already attached to the image or an attached process holds exclusive access
Inputs	One grayscale or color still or sequence, in any integer or floating representation; optional enabled active target mask; 1–11 detail layers plus one residual, fewer for some algorithm and spacing combinations
Outputs	Replaces the target with the same geometry, channel count, and representation; on a still Apply only, optional dark/bright deringing-map stills open beside it; Preview snapshots are auxiliary stills
Default state	Multiscale Linear Transform, Dyadic, 6 detail layers, all layers enabled at bias 0, all optional processing groups off, global Amount 1, Processed Image preview, Preview area on
Recommended image state	A duplicate linear image for noise/detail work. LSTF and DRE are nonlinear display/range operations; derived color components can change reconstructed RGB colors.
Preview support	Asynchronous processed preview that runs what Apply runs (over the Preview area, what Apply makes of that area), three selected-layer diagnostic modes, Linear Mask display, original/result switch, snapshot, zoom, autostretch, and display-channel selection. Global Amount and the active target mask post-blend every preview mode, including layer and mask diagnostics.
Sequence support	Every frame is processed as Apply processes a still image of it, into a temporary replacement sequence, with progress and Cancel; settings are captured once for the run; deringing maps are not made for sequence frames
Mask support	Two distinct masks: Linear Mask weights thresholding inside the transform; the target's active mask blends the final result afterward, together with global Amount
External dependencies	None outside the deployed application; the transform is the bundled AfterNight engine's, and the window's layer arithmetic runs as engine PixelMath programs on the threads the run is granted

Before you start

Duplicate the target and inspect it at 100% with a stable display stretch. Note whether an active target mask is enabled: it affects the committed/processed result but is not the same as Linear Mask. Decide whether the task needs noise/detail changes on the detail layers or a tone change on the residual.

Use Processed Image to judge the real pipeline. The three Layer preview modes are signed coefficient visualizations, not isolated simulations of the enabled layer, noise reduction, deringing, masks, LSTF, or DRE. At zero layer bias they are flat mid-gray or black by design.

The transform refuses a depth it cannot build rather than narrowing it. With Dyadic spacing, the Multiscale Linear Transform accepts at most 7 detail layers and the Starlet Transform at most 10; use Linear spacing for more.

Procedure

1. Activate a duplicate and open Process > Multiscale > Multiscale Linear Transform. Confirm Target Image, Channel, active-mask state, and checked Preview.
2. Leave Multiscale Linear Transform, Dyadic, and 6 Detail Layers for a first pass. Choose Starlet Transform only when a specific scaling kernel is part of the intended model. Use Linear spacing when evenly increasing supports, or more layers than Dyadic accepts, are required.
3. In the layer tree, select a detail layer. Toggle Enabled to locate the relevant scale, or use a small Bias. Compare at 100%; positive bias is a strong nonlinear UI mapping, not a simple 1 + bias gain.
4. For noise reduction, enable the selected layer's Noise Reduction, start at Threshold 3, and reduce Amount before adding Iterations. Use Copy to All only after checking which details should share the setting.
5. If noise reduction should follow brightness, enable Linear Mask and use Preview Mask to inspect it. Remember that this mask weights per-layer and k-Sigma thresholding only; it does not protect bias, LSTF, DRE, or deringing.
6. Use k-Sigma for one threshold policy across every detail layer. Compare Soft versus hard thresholding; enable Use MRS only when robust iterative estimation of the first-detail noise scale is useful.
7. Enable Deringing only for visible edge overshoot. Keep dark/bright values low. On a still, request maps when their layer-stage corrections need inspection; they open beside the target after the result lands. No maps are made by Preview, snapshots, or sequence Apply.
8. Adjust the residual with LSTF only when a nonlinear residual tone mapping is intended. Use Low Range/High Range last because DRE remaps and clamps the reconstructed result.
9. Return to Processed Image, compare original/result, inspect several regions at 100%, then use Apply. Check Image History but save the full settings separately: history is only a summary and omits per-layer values.

Complete parameter and action reference

UI label/action	Type and unit	Runtime default	Persisted-default exception	Valid values, step, or constraints	Effect of increasing, decreasing, or selecting	Dependencies and enable/visibility rules	Quality, artifact, runtime, memory, or disk trade-off	Scope: preview/apply, channel, mask, still/sequence	Persistence
Algorithm	Selector	Multiscale Linear Transform	None	Starlet Transform, Multiscale Linear Transform	Chooses recursive à trous/starlet smoothing or Gaussian smoothings of the original image	Scaling Function enabled only for Starlet Transform	The two have different scale responses and different depth limits; changing it rebuilds layers and noise weights	Preview/Apply; selected channel(s)	Captured; Reset/success Multiscale Linear Transform
Detail Layers	Integer	6	None	1..11; step 1; residual is added automatically. The transform refuses a deeper layer than it can build: with Dyadic spacing at most 7 for Multiscale Linear Transform and 10 for Starlet Transform; with Linear spacing, Multiscale Linear Transform needs (Detail Layers − 1) × Linear Scale ≤ 95	Adds finer-to-coarser detail bands before the residual	Rebuilds layer tree	More layers increase transform, threshold, memory, and reconstruction work; a refused depth shows an error in Preview and Apply	Preview/Apply	Captured; Reset/success 6
Layer Spacing	Selector	Dyadic	None	Dyadic, Linear	Dyadic doubles the scale per layer (1, 2, 4, …); Linear adds Linear Scale per layer (1, 1+q, 1+2q, …)	Linear Scale visible only for Linear	Larger scales represent coarser structure. The Multiscale Linear Transform's Gaussian radius grows with the scale and is refused above 128 pixels; Starlet keeps a fixed tap count and spreads the taps up to 512 pixels apart	Preview/Apply	Captured; Reset/success Dyadic
Linear Scale	Integer	1	None	1..16; step 1	In Linear spacing, raises the scale increment between consecutive layers	Visible only when Layer Spacing is Linear	Larger values separate scales faster and reach the Multiscale Linear Transform's depth limit sooner; they do not change Starlet's tap count	Preview/Apply	Captured; Reset/success 1
Scaling Function	Selector	B3 Spline (5)	None	Linear Interpolation (3), B3 Spline (5), Gaussian (5), Gaussian (7), Gaussian (9), Gaussian (11), Small Scale ¾/⅚/8/12/16/24/32 (3)	Selects the normalized starlet smoothing kernel	Enabled only for Starlet Transform; ignored by the Multiscale Linear Transform	Wider kernels smooth more broadly and cost more	Starlet Preview/Apply	Captured; Reset/success B3 Spline (5)
Global Amount	Double + slider	1.00	None	0..1; spin step 0.05; slider 0..1000	Mixes original (0) to the fully processed result (1)	Transform still runs at 0	Lower values soften every change together; full processing cost remains	Preview/Apply; blended with the active target mask after the process	Captured; Reset/success 1
Layer tree (En / Layer / Bias / NR)	Tree/table	Layers 1–6 + Residual; all enabled, bias 0, NR off	None	One row per detail plus Residual; single selection	Selects the inspector row and summarizes enabled/bias/NR state	Residual has no per-layer NR (—)	More detail layers add rows and processing	Preview/Apply settings	Rebuilt on layer-count change; Reset/success defaults
Enable All	Button	—	None	Click	Enables every detail and the residual	Transform controls enabled outside Apply	Restores all bands but not their biases/NR settings	Preview/Apply settings	Until changed/reset
Disable All	Button	—	None	Click	Disables every detail and the residual	Transform controls enabled outside Apply	Reconstructs zero before later range stages; useful only diagnostically	Preview/Apply settings	Until changed/reset
Reset Biases	Button	—	None	Click	Sets every layer bias to 0	Does not change enabled or NR state	Removes layer gains without removing suppression/NR choices	Preview/Apply settings	Until changed/reset
Linear Mask	Checkable group	Off	None	Off/on	Builds an intensity mask from the processed channel that weights threshold Amount pixel by pixel	Built and used only when per-layer NR or k-Sigma is active	Adds one mask plane and an exact Gaussian smoothing per channel	Preview/Apply; processed channel; separate from target mask	Captured; Reset/success off
Amplification	Integer + slider	100	None	1..300; step 1	Raises A*x before mask clamping, making more samples reach full mask weight	Linear Mask group	High values saturate most of the mask and reduce tonal selectivity	Threshold weighting/Preview Mask	Captured; Reset/success 100
Smoothness	Double + slider	1.0 px sigma	None	0..10; step 0.1	Gaussian-smooths the mask with this sigma; 0 leaves it unsmoothed	Linear Mask group	More smoothing broadens transitions and adds convolution work	Threshold weighting/Preview Mask	Captured; Reset/success 1
Preview Mask	Checkbox	Off	None	Off/on	Shows each processed channel's Linear Mask in place of the processed preview; takes precedence over the Layer preview modes	Linear Mask group must be checked; does not change Apply; shared global Amount and active-target-mask blending still run afterward	Hides the processed transform, but Amount below 1 or an active target mask mixes original pixels into the displayed diagnostic	Preview/snapshot display only; post-blended by global Amount and target mask	Window lifetime; Reset/success off
Inverted	Checkbox	Checked	None	Off/on	Uses 1 - clamp(A*x) before smoothing	Linear Mask group	Reverses which intensity range receives more thresholding	Threshold weighting/Preview Mask	Captured; Reset/success checked
k-Sigma	Checkable group (k-Sigma Thresholding)	Off	None	Off/on	Applies one sigma-threshold policy to every detail after per-layer NR	Detail layers only; residual excluded	Can remove weak real detail together with noise	Preview/Apply	Captured; Reset/success off
Threshold (k)	Double + slider	3.0 sigma	None	0..10; step 0.1	Raises or lowers the global k*sigma threshold	k-Sigma group	Higher values suppress a wider coefficient range	Preview/Apply; all detail layers	Captured; Reset/success 3
k-Sigma Amount	Double + slider	1.00	Header initializer says 0.5, but live initialization and Reset set 1.0	0..1; step 0.05	Blends unthresholded (0) to thresholded (1) coefficients	k-Sigma group; multiplied by the Linear Mask weight when enabled	Lower values retain more coefficient energy	Preview/Apply	Captured; Reset/success 1
Soft Threshold	Checkbox	Checked	None	Off/on	On shrinks magnitudes beyond threshold; off zeros magnitudes strictly below threshold	k-Sigma group	Soft is smoother but biases retained magnitudes; hard can look harsher	Preview/Apply; all details	Captured; Reset/success checked
Use MRS	Checkbox	Off	None	Off/on	Refines the first-detail noise estimate three times using coefficients whose magnitude is at most k*sigma	k-Sigma group	Adds robust-estimation passes; it is not a persistent multiresolution support mask	Preview/Apply	Captured; Reset/success off
Deringing	Checkable group	Off	None	Off/on	Enables edge-weighted coefficient attenuation and a post-reconstruction overshoot correction	Effective when Dark or Bright is above 0	Can soften legitimate high-contrast detail	Preview/Apply	Captured; Reset/success off
Dark	Double + slider	0.10	None	0..1; step 0.05	Reduces negative detail coefficients and negative reconstruction differences near edges	Deringing group	Higher values suppress dark halos but can flatten dark edge structure	Preview/Apply	Captured; Reset/success 0.1
Bright	Double + slider	0.00	None	0..1; step 0.05	Reduces positive detail coefficients and positive reconstruction differences near edges	Deringing group	Higher values suppress bright halos but can flatten highlights	Preview/Apply	Captured; Reset/success 0
Output Deringing Maps	Checkbox	Off	None	Off/on	Requests both dark and bright layer-stage correction maps, opened beside the target after the result lands	Still Apply only; ignored in Preview, snapshots, and sequence processing; both maps are made when the corresponding strength is 0	Adds two Float32 map images and views; a zero-strength side produces an all-zero map	Still Apply; selected processed channel or component	Captured; Reset/success off
LSTF Mode	Selector (Large-Scale Transfer Function)	None	None	None, Hyperbolic, Log10, Natural Log (ln)	Maps the weighted residual before reconstruction	Breakpoint shown only for Hyperbolic; no effect when the residual is disabled	All non-None modes are nonlinear and clamp the weighted residual to [0,1]	Preview/Apply; residual only	Captured; Reset/success None
Breakpoint	Double + slider	0.75	Builder starts at 1.0, but live initialization and Reset set 0.75	0.1..1; step 0.05	In Hyperbolic mode, smaller values brighten more strongly	Visible only for Hyperbolic	White maps below 1; not a normalized endpoint-preserving stretch	Preview/Apply; residual only	Captured; Reset/success 0.75
Low Range	Double + slider	0.00	None	0..1; step 0.05	Adds to reconstructed values before division by total range	Always available (Dynamic Range Extension)	Shifts values upward while the shared denominator compresses the range	Preview/Apply; after reconstruction/deringing	Captured; Reset/success 0
High Range	Double + slider	0.00	None	0..1; step 0.05	Enlarges the denominator without adding to the numerator	Always available (Dynamic Range Extension)	Compresses highlights/dynamic range; result is clamped	Preview/Apply; after reconstruction/deringing	Captured; Reset/success 0
Selected Layer	Group title and read-only label	Layer 1	None	Layer n, Residual Layer, or No layer selected	Identifies which layer the inspector edits	Changes with tree selection	Avoid editing the wrong spatial scale	Settings and layer diagnostic preview	Window lifetime
Selected-layer Enabled	Checkbox	Checked	None	Off/on	Includes (on) or removes (off) the selected layer in reconstruction	Applies to residual too	Disabling a layer can remove real structures; disabling residual removes the base image	Preview/Apply	Captured per layer; Reset/success checked
Copy to All	Button	—	None	Click	Copies selected Enabled and Bias to every row; copies NR only between non-residual details	Residual never receives NR; copying from Residual leaves detail NR unchanged	Broad changes can erase carefully tuned scale differences	Preview/Apply settings	Until changed/reset
Reset Layer	Button	—	None	Click	Resets selected row to enabled, bias 0, NR off, threshold 3, Amount 0.5, iterations 1	Residual NR remains unavailable	Per-layer NR Amount becomes 0.5, unlike full Reset/live startup 1.0	Preview/Apply settings	Until changed/full reset
Bias	Double + slider	0.00	None	-1..15; spin step 0.01; paired slider spans negative/positive adjustment	-1 removes the layer; negative values attenuate; positive values strongly amplify	Applies to selected detail or residual	Positive UI values map to 6× gain increments, 8× on the Multiscale Linear Transform's first detail; clipping/ringing can grow quickly	Preview/Apply; layer diagnostic uses a separate display gain of 5× bias	Captured per layer; Reset/success 0
Selected-layer Noise Reduction	Checkable group	Off	None	Off/on	Enables repeated soft thresholding for selected detail	Disabled/unavailable for Residual	Can smooth noise and weak structures at that scale	Preview/Apply; detail layers only	Captured; Reset/success off
NR Threshold (σ)	Double + slider	3.0 UI sigma	None	0..40; step 0.1; the threshold is 0.05 of the UI value in noise deviations	Raises the coefficient threshold used for selected-layer shrinkage	Selected-layer NR	Higher values remove more coefficient energy	Preview/Apply; weighted by the Linear Mask when enabled	Captured; Reset/success 3
NR Amount	Double + slider	1.00 at startup/full Reset	Reset Layer sets 0.50; layers added by raising Detail Layers also start at 0.50	0..1; step 0.05	Blends each shrinkage pass from original to thresholded coefficient	Selected-layer NR	Lower values soften each pass	Preview/Apply; weighted by the Linear Mask when enabled	Captured; full Reset 1, layer Reset 0.5
NR Iterations	Integer	1	None	1..10; step 1	Repeats shrink/blend on the already changed coefficient	Selected-layer NR	More passes increase suppression and work; no re-decomposition between passes	Preview/Apply	Captured; Reset/success 1
Target Image	Image/sequence selector	Attached active target	None	Any target accepted by launch guards	Changes destructive destination, active mask, channels, and preview	Disabled during Apply	Wrong target is overwritten	Preview/Apply; still/sequence	Target lifetime; Reset unchanged
Channel	Selector	RGB, or a disabled Grayscale for a grayscale target	None	Grayscale; RGB, Red, Green, Blue, CIE L* (Lightness), CIE a, CIE b, CIE c, CIE h, CIE X, CIE Y (Luminance), CIE Z, HSL Hue/Saturation/Lightness, HSV Hue/Saturation/Value, YCbCr Luma/Blue Chroma/Red Chroma	RGB transforms the stored channels independently; another choice is extracted, transformed, then recomposed into the color image	Non-grayscale choices only for color targets; disabled during Apply	Derived conversion/recomposition adds work and can alter out-of-gamut colors	Preview/Apply	Captured; target-dependent; Reset unchanged
Preview	Checkbox	Checked	None	Off/on	Enables asynchronous live preview	Stays available during Apply; Apply cancels a preview in progress	Recomputes after parameter edits; a burst of changes collapses into one run with the latest values	Preview only; active-target-mask-aware	Window lifetime; Reset unchanged
Preview mode	Selector	Processed Image	None	Processed Image, Layer (All Changes), Layer (Increasing Pixels), Layer (Decreasing Pixels)	Selects real pipeline or signed selected-layer visualization (the residual can be shown too)	Enabled only while Preview is checked; global Amount and the active target mask post-blend the selected visualization; Preview Mask takes precedence	Layer modes are diagnostics, not reconstructed output; Amount or a target mask can mix the original into them	Preview/snapshot only	Reset/success Processed Image
Preview pane	Image viewer	Processed result over the Preview area	None	Standard pan/scroll and actions below	Shows processed or diagnostic output without commit	Exists while Preview checked	Holds source/result/display buffers	Preview only	Window lifetime
Fit To Window	Preview action	Fitted initially	None	Click or Ctrl+Shift+F	Fits whole image	Preview required	Broad context can hide small-scale effects	Display only	Viewer lifetime
Zoom In	Preview action	Current scale	None	Click; 1.25×	Enlarges view	Preview required	Better coefficient/noise inspection	Display only	Viewer lifetime
Zoom Out	Preview action	Current scale	None	Click; 0.8×	Reduces view	Preview required	More context, less pixel detail	Display only	Viewer lifetime
Zoom 100%	Preview action	Current scale	None	Click; scale 1.0	Shows one-pixel viewer scale	Preview required	Best for noise, halos, and ringing	Display only	Viewer lifetime
View Channel	Preview selector	Follows result	None	Supported stored/derived display components	Changes displayed component only	RGB choices require RGB result	Helps isolate channel-dependent artifacts	Display only	Viewer lifetime
Display Mode	Preview selector	Linear	None	Linear, Autostretch	Changes display transfer only; Autostretch measures the image's median and MAD exactly and rounds each display byte to the nearest code	Preview required	Autostretch can exaggerate threshold residuals	Display only	Preview lifetime
Autostretch Settings	Preview action	Initialized from target view	None	Opens display settings	Adjusts Autostretch only	Relevant in Autostretch mode	Adds display/statistics work	Display only	Preview lifetime
Switch image	Preview action	Result shown	None	Click, Space, right-click, or Ctrl+Shift+O	Toggles result/original	Preview required	Direct structure/noise comparison	Preview/current frame	Preview lifetime
Preview area	Preview checkbox/region	Checked when the Preview opens; centered, at most 1200×1200 (the whole image when smaller)	None	Off/on; movable supported area	Runs the preview over the area only, as Apply would over an image of that area, and shows the image as it was around it	Disabled during Apply; Apply processes the full frame	Reduces tuning work; large-scale layers near the area's edge see the area's border rather than the rest of the image	Preview/snapshot only	Window lifetime
Take snapshot	Preview action	No snapshot	None	Click or Ctrl+Shift+K	Runs the current settings again as a preview and opens <target> - Multiscale Linear Transform - SNAPSHOT; with Preview area on, the snapshot is the composite the Preview showed	Preview required; disabled during Apply	Adds processing/allocation; target unchanged; a Layer or Preview Mask mode is what is taken; no deringing maps	New still	One view per action
Apply	Dialog action	Enabled	None	One click	Captures parameters, processes the full target (still or every frame), and replaces it after success	Transform/layer/global/inspector groups, Target, Channel, Close, Reset, and the Preview pane's snapshot and area actions are disabled during the run; Preview and the preview-mode selector stay available; a second Apply is ignored while busy	Destructive; work scales with pixels, channels, layers, support, thresholds, and iterations	Still/sequence; active-target-mask-aware	Adds one summary history step; resets process settings after success
Close	Dialog action	Enabled	None	One click	Closes without starting Apply	Disabled while Apply runs	Use Cancel in the progress dialog to stop a run	Dialog	Discards UI state
Reset	Dialog action	Enabled	None	One click	Restores live defaults and schedules Preview	Disabled while Apply runs	Can trigger a full preview transform	UI/preview	Immediate; also after success; Target/Channel/Preview retained
Apply progress / Cancel	Shared progress dialog	Created on still and sequence Apply	None	Cancel	Stops the run at the engine's next checkpoint: the target is not replaced, no map opens, and no error is shown; a sequence run also removes its temporary output	Apply only	A long transform pass can finish before the stop is observed; sequences also incur temporary disk/codec cost	Still/sequence Apply	Target unchanged after Cancel

How the algorithm works

Decomposition, spacing, and boundaries

Let c_0 be one processed channel in normalized units. With detail-layer index l starting at zero, AfterNight uses the scale

• s_l = 2^l for Dyadic, or
• s_l = 1 + lq for Linear, where q is Linear Scale.

The Starlet Transform smooths the current coarse layer with the selected separable kernel, its taps spread s_l pixels apart, then stores w_l = c_l - c_(l+1). The Multiscale Linear Transform instead smooths the original c_0 at each scale with a Gaussian of sigma = s_l/3, truncated at four standard deviations (radius ceil(4 sigma)), and stores the difference between consecutive smoothings, the first detail being c_0 minus the finest smoothing. In both cases the last smoothing is the Residual, and the details plus the residual add back to the input to single-precision rounding when every weight is 1.

Starlet kernels are normalized: Linear Interpolation [1,2,1]/4, B3 Spline [1,4,6,4,1]/16, odd Gaussian supports 5/7/9/11 with sigma = radius/3, and Small Scale n uses [1,n,1]/(n+2). Every smoothing repeats the nearest edge sample beyond the frame. Neither algorithm is decimated: every layer retains full image geometry.

The transform refuses a depth it cannot build, rather than quietly using a narrower filter: a Starlet layer whose taps would be more than 512 pixels apart, or a Multiscale Linear Transform layer whose Gaussian radius would exceed 128 pixels. Preview and Apply then show an error saying that the deepest layer needs a tap spacing or a Gaussian radius above the stated maximum, and to ask for fewer layers or a smaller linear step. With Dyadic spacing this allows at most 10 Starlet and 7 Multiscale Linear Transform detail layers; with Linear spacing, Starlet accepts all 11 at every Linear Scale, and the Multiscale Linear Transform accepts (Detail Layers − 1) × Linear Scale ≤ 95.

Layer enablement, bias, and reconstruction

An unchecked layer is removed (weight 0). For an enabled layer with bias b <= 0, the weight is 1+b, so -1 removes it and 0 preserves it. Positive bias uses the current AfterNight gain mapping:

• Starlet Transform: 1 + 6b;
• Multiscale Linear Transform first detail: 1 + 8b;
• other Multiscale Linear Transform details and its residual: 1 + 6b (the residual uses 1 + 8b when there is a single detail layer).

This source behavior is stronger than the inspector tooltip's simple 1 + bias description. The weights apply when the layers are added back, after thresholding and deringing. When LSTF is on, the residual's weight is applied before the transfer and the transferred residual is added back with weight one. The output is the sum of the weighted details and the residual.

Noise reduction, k-Sigma, and the Linear Mask

Each channel's first-detail noise deviation is the robust scale sigma_1 = median(|w_0|)/0.67448975. The noise of every other layer is sigma_1 times that layer's share of white noise relative to the first layer's. A layer's share is the norm of its response to a single bright pixel, measured once per run by decomposing an impulse at the center of a square of 512 to 1024 pixels with the same transform. It is deterministic and the same on every build. If the first detail's median is zero, each layer's deviation is measured on its own coefficients.

Selected-layer NR converts the displayed threshold t to 0.05t, multiplies it by the larger of sigma_1 and the layer's own deviation, soft-shrinks the coefficients, and blends by Amount. Iterations repeat that shrink/blend on the changed coefficient; they do not re-decompose the image.

Global k-Sigma follows per-layer NR. For each detail and threshold T = k sigma_l, Soft computes sign(w) max(|w|-T,0), while hard thresholding sets |w| < T to zero (a coefficient exactly at T survives), and the result is blended by k-Sigma Amount. Use MRS re-estimates sigma_1 three times from the first-detail coefficients whose magnitude is at most k sigma_1. It refines that noise estimate only; it does not build a persistent multiresolution-support map.

When enabled, Linear Mask starts from the processed channel: m = clamp(Ax,0,1), optionally replaces it by 1-m, smooths it with an exact Gaussian of the chosen sigma, and clamps again. Each shrinkage then blends by Amount × m pixel by pixel. This mask affects both per-layer NR and k-Sigma, but not layer bias, deringing, LSTF, DRE, or the final target-mask blend. If neither thresholding mode is active, it is not built and changes no normal output; Preview Mask can still display it.

Deringing, residual stretch, and range mapping

Deringing builds a per-channel edge weight from the channel itself: the larger of the absolute horizontal and vertical central differences, the edge sample repeated beyond the frame. It is normalized by its 90^th percentile, or by its maximum when that percentile is below 0.001, and clamped to [0,1]; an image whose maximum edge is also below 0.001 has no edge to speak of, and deringing then changes next to nothing. After thresholding, each detail coefficient w becomes w + D e max(0,-w) - B e max(0,w), where D is Dark, B is Bright, and e the edge weight. The optional maps add up these nonnegative layer-stage corrections over every detail layer. After reconstruction, a second edge-weighted pass moves the result y toward the original x: y + D e max(0,x-y) - B e max(0,y-x). That second pass is not accumulated in the map views.

LSTF changes the residual after its weight c, with v = clamp(c R,0,1):

• Hyperbolic: f(v) = v/(v+b) for Breakpoint b;
• Log10: f(v) = log10(1+9v);
• Natural Log: f(v) = ln(1+(e-1)v).

Hyperbolic does not preserve white: f(1)=1/(1+b). Log10 and natural log brighten normalized midtones; all three make the pipeline nonlinear.

After reconstruction and post-deringing, DRE maps

y = clamp((x + Low Range)/(1 + Low Range + High Range), 0, 1).

With both controls at zero the result is still clamped to [0,1]: without Deringing or DRE the reconstruction itself is clamped, so every result lies in [0,1].

Channel, precision, preview, and masks

The run works on the channel or color component the selector names. RGB processes each stored channel independently. A selected Red/Green/Blue or derived CIE/HSL/HSV/YCbCr component is extracted, transformed, and recomposed with the other components; derived-component conversion can introduce rounding and out-of-gamut clipping.

Samples are read in normalized units: an unsigned integer divided by its largest code, a signed integer counted from its smallest code to its largest, and a floating sample as it is. Integer images are converted into a floating working copy (Float64 for 32-bit integers) and the result is narrowed back to the original representation, rounding to the nearest code. The transform and its layer arithmetic work in single precision on every representation. Floating values outside [0,1] do not survive, because the result is clamped.

A sample holding NaN or an infinity does not stop the run: the transform counts it as zero for its neighbors while it decomposes the image, and the result leaves that sample as it was. Samples that the image's own validity marks as not valid are treated the same way.

Processed preview runs what Apply runs, over the target or the Preview area; inside the area the Preview is what Apply makes of an image of that area. Layer modes instead decompose the unprocessed source and display the selected row's coefficient w (the residual can be selected too) times k = 5 × Bias: All Changes shows clamp(0.5 + kw), Increasing Pixels clamp(k max(0,w)), and Decreasing Pixels clamp(k max(0,-w)). The layer visualization ignores Enabled, NR, k-Sigma, Linear Mask, deringing, LSTF, and DRE. At Bias 0, All Changes is therefore mid-gray and the sign-only modes are black before shared preview blending; a negative Bias inverts All Changes and leaves the sign-only modes black.

After any process-local preview result is produced—including a layer mode or Preview Mask—the shared framework applies global Amount and the active target mask. Amount 0 therefore shows the original source rather than the raw diagnostic, and protected target-mask pixels also show the original. Use Amount 1 and disable the active target mask when an unmixed layer or Linear Mask diagnostic is required.

The target's enabled active mask blends original and result after the process, together with global Amount. Its inversion/weight is independent of the Linear Mask inside the noise-threshold stages. Each engine operation observes the run's stop request; a stopped run publishes nothing.

Parameter interactions and starting points

• Locate scale before applying gain: temporarily disable one layer at a time or inspect its signed preview, then return to Processed Image.
• Positive Bias is deliberately strong. Start near zero and watch both sides of high-contrast edges; use global Amount to reduce the combined result.
• Per-layer NR is for different thresholds by scale. k-Sigma is an additional pass across every detail, so enabling both compounds suppression.
• Linear Mask only weights threshold Amount. Use the target's active mask when bias, deringing, residual stretch, DRE, or the whole final result needs spatial protection.
• Deringing maps show the layer-stage correction, not every change responsible for the final deringed image.
• Set global Amount to 1 and disable the active target mask when inspecting a raw Layer or Preview Mask diagnostic; both shared blends run after the process-local preview mode.
• Apply LSTF to the residual before DRE. DRE then remaps and clips the entire reconstruction, including altered details.
• More depth needs Linear spacing: Dyadic stops at 7 Multiscale Linear Transform or 10 Starlet detail layers, and a larger Linear Scale lowers the Multiscale Linear Transform's limit.

Inputs, outputs, and metadata

A still result keeps source geometry, channel count, representation, and all of its metadata: every FITS card, the astrometric solution, the acquisition record, and the image's stated meaning. It is not recorded as nonlinear, even when LSTF, DRE, clipping, or derived-channel recomposition made it so. The image's lineage gains an entry naming an::reconstructImageMultiscale with the history description.

A sequence is processed frame by frame into a temporary replacement, each frame as Apply processes a still image of it; configured CFA auto-debayering may supply RGB frames through the shared sequence path. The same captured settings are used for every frame. Apply shows a progress dialog with Cancel for both stills and sequences. Cancel prevents replacement; a sequence Cancel also removes the temporary output.

On a still Apply only, requested deringing maps open beside the target once the result has landed, named from the target plus - Deringing Dark Map or - Deringing Bright Map. On a color target whose Channel is not RGB, the channel follows in parentheses, for example M42 - Deringing Dark Map (Red). Each map is a Float32 image with one channel per processed channel or component, and its processing-state cards record it as nonlinear, set by a process, under multiscale-deringing-dark-map or multiscale-deringing-bright-map. The maps keep the target's acquisition record, solution and lineage but none of its other cards, and their history starts with Multiscale Linear Transform - Deringing Dark Map or ... Bright Map. They are not created for Preview, snapshots, or sequence frames.

Image History records one step named Multiscale Linear Transform, for example Algorithm: Multiscale Linear Transform, Layers: 3, Spacing: Dyadic in channel: RGB. It summarizes algorithm, layer count, spacing (Linear (scale q) for Linear), Starlet scaling function, the values of each enabled optional group, DRE, and, on a color target, the channel. It omits individual layer enable/bias/NR values and global Amount, so it is not a complete recipe.

Settings live only for the process window. Reset restores runtime defaults; a successful Apply also resets process settings while retaining Target, Channel, and the Preview checkbox. There is no process preset/file persistence in this dialog.

Performance

Runtime grows approximately with pixels × processed channels × layers × effective kernel work. Starlet support is the selected kernel spread by the layer's scale, but its tap count stays fixed. The Multiscale Linear Transform's Gaussian radius grows with the scale up to the 128-pixel limit. Per-layer iterations, MRS estimation, k-Sigma, mask smoothing, deringing, and derived-color conversion add passes; thresholding also decomposes one impulse image of 512 to 1024 pixels a side per run. The engine runs on the threads the run is granted and observes a stop request within its passes, not at every sample.

A decomposition holds every layer at once: width × height × processed channels × (Detail Layers + 1) × 4 bytes. A run adds a single-precision copy of the processed samples, three single-channel scratch planes, a single-precision result, and, for an integer image, a floating working copy. Increasing layers costs more memory even if some rows are disabled, because decomposition occurs before reconstruction choices. Preview holds additional source/result/display buffers, and a Preview area reduces the work to the area. Sequence Apply also uses temporary encoded storage. A run the session's memory budget cannot hold is refused with an error naming the memory budget, and nothing is published. No production timing or peak-memory benchmark was run for this page.

Worked example

• Evidence mode: source/equation-derived; no astronomical data was run.
• Start with a normalized constant grayscale field c_0 = 0.25, either algorithm, any supported spacing, every layer enabled, Bias 0, and all optional groups off. Every detail is zero because each kernel sums to one and the repeated edge keeps the field constant at the borders, while the residual remains 0.25; reconstruction is 0.25. The engine's decomposition is a partition whose layers add back to the input to single-precision rounding.
• Disable only the residual. With all zero details, Processed Image becomes zero before global Amount/active-mask blending. At global Amount 0.5, no active target mask, the final checkpoint is 0.125 because the shared blend mixes the original and zero reconstruction equally.
• On real linear data, use this same reasoning as a diagnostic: if disabling a layer changes structures far from the expected scale, reconsider Algorithm, spacing, and support before adding Bias or thresholding. This example does not establish visual quality on astronomical images.

Warnings and limitations

• Apply replaces the still or sequence. Work on a duplicate and verify Target.
• Positive Bias is mapped much more strongly than the current tooltip implies.
• LSTF, DRE, clipping, and many derived-component recompositions are nonlinear; the main output keeps the source's metadata and is not recorded as nonlinear.
• Every result is clamped to [0,1]; floating values outside that range do not survive Apply.
• A depth the transform cannot build is refused with an error, not narrowed. The dialog offers eleven detail layers, but Dyadic spacing stops at 7 (Multiscale Linear Transform) or 10 (Starlet Transform).
• Disabling the residual removes the coarse base; disabling all layers produces zero before later mappings and blends.
• Layer previews are diagnostic coefficient displays, not previews of isolated production stages.
• Linear Mask is not the target's active mask and cannot protect bias, deringing, LSTF, or DRE.
• Deringing maps omit the post-reconstruction correction and are made only by a still Apply.
• Cancel is observed at the engine's next checkpoint, so the current pass may finish first, but the target is not replaced afterward.
• The worker captures settings for Apply, but Preview and the preview-mode selector are not locked with the main settings groups. They do not change the captured Apply parameters.
• History is incomplete for reproduction. Save settings separately.
• A run the engine refuses (a depth it cannot build, or more memory than the session's budget) shows the reason and leaves the target unchanged.

Troubleshooting

Symptom/question	Verified interpretation or cause	Resolution/next page	Evidence source
Error says the deepest layer needs a Gaussian radius or a tap spacing above the stated maximum	The Detail Layers, spacing, and Linear Scale ask for a layer deeper than the transform can build	Use fewer Detail Layers, Linear spacing, or a smaller Linear Scale	planMultiscaleTransform in MultiscaleTransform.cpp; process_utils::multiscale::planTransform
Layer preview is flat gray or black	Bias 0 gives zero visualization gain; All Changes centers zero at gray and sign-only modes clamp to black	Change Bias slightly for diagnosis, or return to Processed Image for real output	process_utils::multiscale::previewLayerInPlace
Scaling Function has no effect	The Multiscale Linear Transform builds a Gaussian from the scale and ignores the Starlet kernel selector	Choose Starlet Transform when a listed scaling function is required	MultiscaleExecution.cpp smoothing; UI algorithm-state update
Result is much stronger than the Bias number suggests	Positive bias maps to 1+6b, or 1+8b on the Multiscale Linear Transform's first detail	Start near zero; compare at 100%; reduce global Amount	process_utils::multiscale::layerWeight
Linear Mask changes nothing	It weights only per-layer NR/k-Sigma; neither may be enabled	Enable the intended thresholding stage, or use the target active mask for whole-result protection	process_utils::multiscale::transformInPlace mask/threshold order
Noise reduction is unexpectedly strong	Per-layer NR and k-Sigma run sequentially; Iterations repeat shrinkage; Linear Mask may be inverted	Disable one threshold stage, restore Iterations 1, inspect Preview Mask and inversion	process_utils::multiscale::transformInPlace
Reset Layer gives Amount 0.5 instead of startup 1.0	The per-layer reset path assigns 0.5; full Reset/live initialization assigns 1.0	Set the intended value explicitly; use full Reset for startup defaults	MultiscaleLinearProcess.cpp reset paths
Hyperbolic white becomes darker	f(1)=1/(1+b); this implementation does not normalize the endpoint back to 1	Compare None/Log10/ln or follow with intentional DRE	process_utils::multiscale::transformInPlace residual transfer
Deringing map does not explain every final correction	Maps contain only layer-stage corrections, not the post-reconstruction pass	Treat maps as diagnostics, not an exact final-difference image	process_utils::multiscale::transformInPlace deringing stages
A deringing map is entirely black	Both maps are made on a still Apply whenever Deringing and Output Deringing Maps are enabled; a zero corresponding strength produces a zero map	Raise the relevant Dark/Bright strength if that correction is intended; do not expect maps from Preview/snapshot/sequence	MultiscaleLinearProcess::executeTypedProcessIteration
Active mask and Preview Mask disagree, or Preview Mask resembles the source	Preview Mask selects the internal intensity mask first, then global Amount and the target mask blend original pixels back into the display	Set Amount to 1, disable the active target mask for the diagnostic, then restore the intended settings before Processed Image/Apply	MultiscaleLinearProcess::executeTypedProcessIteration; shared run blend in ImageRTPreviewControl.cpp
Error mentions the memory budget	The decomposition and its working planes do not fit the session's memory budget	Use fewer Detail Layers, a single channel or component, or raise the processing memory limit	MasksWindowTest refusal case; MultiscaleExecution.cpp allocation
Cancel takes time	Cancellation is observed between and within engine passes; the current pass may finish first	Wait for cleanup; reduce layers/support/iterations before retrying	ProgressDialogControl.h; shared run landing in ImageRTPreviewControl.cpp
Image History cannot reproduce the result	It omits per-layer settings and global Amount	Record the layer table and inspector values separately	multiscale_detail::describeTransform

Related workflow steps

• Wavelet Denoise uses a different, decimated Haar analysis for denoising.
• Sharpen Alpha offers a more focused multiscale detail-enhancement workflow.
• Histogram Transformation is the dedicated page for deliberate display stretching after linear processing.
• Masks explains the target active mask that blends the complete process result.

References and provenance

• The AfterNight process, its layer composition, the shared preview/Apply framework, the engine transform, and the focused tests are the authority for this page.
• Algorithm names here describe AfterNight's current implementation. They do not claim parameter or output compatibility with another application's tool of a similar name.