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Adaptive Quality Map Hyperstacking (AQMH) Methodology v0.2.1

Document status: Normative for the v0.2.1 configuration family.
Supersedes: aqmh_methodik_en_v0.2.0.md.
Language: English. For the German version see aqmh_methodik_de_v0.2.1.md.

0. Document History and Scope

0.1 Changes from v0.2.0

Version v0.2.1 is a strict superset of v0.2.0. All mathematical definitions, invariants, normative defaults and diagnostic requirements of v0.2.0 remain binding. v0.2.1 formalises three main additions that were introduced in the reference implementation after the v0.2.0 baseline:

  1. Background-gradient penalty in global frame quality (§1.5, §4.2).
    A third global-quality signal penalises frames with strong large-scale background gradients (e.g. light pollution, moon glow). The signal is derived from a quadrant-based sky-gradient estimator, not from the AQMH quality map itself. It is therefore documented as a permitted cross-infrastructure extension that remains compatible with the AQMH independence principle (§0.4).

  2. Registration-weight guard (§4.3).
    Before the per-pixel weighted reconstruction, each frame's global AQMH weight can be damped by a registration-confidence factor derived from the shared global-registration artifact. This guard is purely a robustness measure; it does not change the reconstruction formula and it remains a frame-level multiplier.

  3. Adaptive low-frequency neutralisation and structure-masked detail blending (§6.3, §6.4).
    After the ordinary AQMH reconstruction, an optional post-processing stage removes low-frequency "veil" residuals by subtracting a heavily blurred difference between the AQMH output and a uniform-control (unweighted) mean. Detail is then selectively reintroduced in high-structure regions. A validation gate decides whether the neutralised/blended result is kept; if not, the raw AQMH output is preserved. Uniform control must never silently replace or attenuate raw AQMH.

The goal of these additions is to preserve the v0.2.0 pixel-quality model while reducing three practical failure modes:

  • Large-scale background gradients that would otherwise dominate the final stack because every frame shares a similar additive gradient.
  • Residual registration weakness (low correlation or deep chain-predicted frames) being amplified by high AQMH quality scores.
  • Low-frequency "veil" or background non-linearity introduced by the weighted reconstruction itself.

0.2 Gate Applicability Clarification (2026-07-18)

The validation gates introduced by v0.2.1 are only meaningful for metrics that are finite and comparable in both the AQMH candidate and the uniform control. A metric whose control value is non-finite, missing, or numerically degenerate must be reported as not_applicable; it must not be converted into an artificial hard failure.

This clarification is object-agnostic. Implementations must not special-case individual targets or object names. The same applicability rules must work for bright emission nebulae, faint galaxies, large galaxy arms, star clusters, high-latitude dust/IFN fields and sparse star fields. Scene content may affect whether a metric is applicable; it must not change the mathematical meaning of the metric.

In particular:

  • Relative regression must not be computed from a zero or near-zero control denominator without an explicit absolute fallback threshold.
  • null/NaN seam scores are diagnostic values, not valid veto values.
  • Star-tail and elongation gates require enough comparable star samples in both candidates.
  • Final selection may use asymmetric tradeoffs: a clear primary improvement (e.g. FWHM or elongation) may tolerate bounded secondary regressions (background, seam, tail) when those secondary metrics are applicable and reported.
  • Structure preservation must be evaluated over more than the brightest high-gradient pixels. Faint galaxy arms, dust lanes and diffuse nebula structures are valid signal and must not be treated as background solely because their gradients fall below a high global quantile.

0.3 Independence and Shared Infrastructure

AQMH remains an independent reconstruction method. It may reuse shared pipeline infrastructure, but its quality model and reconstruction weights are not derived from Classic Tile Compile local/tile metrics.

Shared infrastructure may include:

  • input scan and non-quality eligibility filtering (readability, calibration availability, explicit user exclusions);
  • calibration and registration/prewarping;
  • global photometric normalization;
  • global output-canvas mask C and frame-specific registered-valid masks M_f;
  • run management, logging, artifacts, reports, UI plumbing.

The AQMH algorithm itself consists of:

  • AQMH dense quality-map computation;
  • AQMH pixel-wise weighted reconstruction;
  • AQMH diagnostics and optional region extraction.

Classic Tile Compile and AQMH must remain runnable independently. Enabling or disabling one method must not change the mathematical definition of the other.

0.4 Cross-Infrastructure Extensions

v0.2.1 explicitly allows the following carefully scoped inputs from shared infrastructure, provided they are documented and do not replace AQMH-native signals:

  • Sky-gradient summary for the background penalty (§1.5).
    This is a scalar per frame, derived from the background-masked input image after registration. It is used only inside the global-quality sigmoid and remains orthogonal to the within-frame Q_map computation.

  • Registration confidence metadata for the weight guard (§4.3).
    This is a scalar multiplier per frame, derived from the existing global registration artifact. It adjusts the global factor G_f but does not influence Q_map.

  • Uniform-control mean for neutralisation validation (§6.3).
    The unweighted mean of the registered frames is computed as a side product of AQMH reconstruction (compute_uniform_control = true). It is used only for post-reconstruction validation, not as a primary quality input or an output candidate.

  • PSF-FWHM sharpness proxy for the global sharpness summary g_sharp (§1.1, §4.2).
    When per-frame star metrics are available from the shared metrics phase, the runner may substitute 1 / wfwhm (weighted FWHM, inverted so that smaller FWHM yields a higher sharpness value) for the AQMH-map g_sharp summary. This is a scalar per frame, derived from PSF star detection on the registered frame. It is used only inside the global-quality sigmoid and remains orthogonal to the within-frame Q_map computation. The AQMH-map g_sharp serves as fallback when star metrics are unavailable or invalid. The selected source is recorded per frame as global_sharpness_source ("laplacian_variance" or "psf_wfwhm_inverted") in aqmh_metrics.json.

Rationale. The AQMH-map sharpness signal Phi_sharp_0 is based on local_variance(laplacian), which measures local high-frequency variance. On stellar-dominated fields this is an excellent sharpness proxy. On extended-emission targets (galaxies, nebulae) the same signal is dominated by nebular texture rather than stellar PSF width, and can correlate positively with seeing FWHM — causing an inversion where worse frames receive higher g_sharp and thus higher weights. The PSF-FWHM proxy is immune to this inversion because it measures stellar image width directly, independent of extended-scene content.

1. Principles and Definitions

1.1 Physical Objective

The method models per-pixel observational quality as the product of two separable components:

  • Frame-level quality: the global atmospheric/technical state of frame f, captured by the strictly positive AQMH factor G_{f,c}.
  • Spatial quality field: the continuous quality distribution within the frame, captured by Q_map_{f,c}(x,y).

For every frame/channel, derive the global pre-z-score summaries from its AQMH maps:

g_sharp_{f,c}  = median_{p source-valid}(Phi_sharp_0(p))
g_snr_{f,c}    = median_{p source-valid}(Phi_snr_1(p))

using the finest available scale if scale 1 is omitted.

Post-v0.2.1 extension — PSF-FWHM sharpness proxy. When per-frame star metrics are available, the runner may replace g_sharp with 1 / wfwhm (inverted weighted FWHM) from the shared PSF star-detection phase. This avoids a known inversion of local_variance(laplacian) on extended-emission targets (§0.4). The AQMH-map g_sharp is used as fallback when star metrics are unavailable. The selected source is recorded per frame as global_sharpness_source ("laplacian_variance" or "psf_wfwhm_inverted") in aqmh_metrics.json.

1.2 Effective Pixel Weight

The effective per-pixel reconstruction weight is:

W_{f,c}^{aqmh}(x,y) = G_{f,c} * Q_map_{f,c}(x,y)

v0.2.1 additionally allows a per-frame registration-confidence multiplier R_f ∈ [r_floor, 1] (§4.3). When enabled, the weight becomes:

W_{f,c}^{aqmh}(x,y) = G_{f,c} * R_f * Q_map_{f,c}(x,y)

R_f is a shared-infrastructure guard, not part of the AQMH quality model. It must be reported in aqmh_reconstruction.json.

1.3 Invariants (Binding)

The following invariants remain binding from v0.2.0:

  1. No frame selection: Entire frames must not be removed based on quality.
  2. Conditional photometric linearity: Once deterministic weights are computed, the final reconstruction remains R(p) = sum_f w_f(p) * I_f(p) / sum_f w_f(p) with w_f(p) >= 0. AQMH must not apply non-linear intensity transforms to the samples entering the accumulator.
  3. Determinism: All quality-map computations must be deterministic and reproducible.
  4. Canvas exclusion: Canvas-invalid pixels are excluded from all AQMH accumulators and statistics.
  5. No hallucination: AQMH outputs are weights and masks only. It does not generate or predict pixel intensities.
  6. Sample-count sufficiency for optional selection modes: Cherry-pick and any other per-pixel selection mode must enforce a documented minimum retained-sample count, below which the mode is disabled automatically.

v0.2.1 adds the following derived invariants for the new extensions:

  1. Cross-infrastructure extensions must be monotonic frame-level guards.
    The registration-weight guard and the background penalty may only multiply the global frame weight by a non-negative scalar. They must not alter Q_map, must not introduce pixel-dependent weights, and must be independently disableable.

  2. Neutralisation must be validation-gated.
    Any post-reconstruction neutralisation or detail blending must be compared against the ordinary AQMH output and/or the uniform-control mean. The run must record which candidate was selected and why. The final output must not be worse, by the documented regression metrics, than the ordinary AQMH output.

1.4 Deterministic Statistics Convention

(Identical to v0.2.0 §1.4.)

Robust z-score is used throughout: z(x) = (x - med) / (1.4826 * MAD) over finite, source-valid samples at the same aggregation level. Degenerate sets (MAD = 0 or fewer than three finite samples) map to z-score 0 for valid inputs and are flagged invalid otherwise.

1.5 Global Quality with Background Penalty (v0.2.1 addition)

v0.2.1 introduces an optional third global-quality signal:

g_background_{f,c} = sky_gradient_f

where sky_gradient_f is a dimensionless relative large-scale gradient:

sky_gradient_f = (q_max - q_min) / background_f
  • background_f is the masked median background of frame f.
  • The image is divided into four quadrants. For each quadrant q the masked median background b_q is computed.
  • q_min = min_q(b_q), q_max = max_q(b_q).

If background_f <= 0 or fewer than four valid quadrant values exist, the summary is invalid.

The background penalty enters global quality as a subtractive term:

z_s,f = robust_zscore(g_sharp)
z_n,f = robust_zscore(g_snr)
z_b,f = robust_zscore(g_background)

score_f = w_sharp * z_s,f + w_snr * z_n,f - w_background * z_b,f
G_f     = g_floor + (1 - g_floor) * sigmoid(clamp(g_k_scale * score_f, -8, 8))

with sigmoid(v) = 1 / (1 + exp(-v)).

Post-v0.2.1 extension — Sigmoid temperature and score clipping. The implementation multiplies score_f by a configurable temperature factor g_k_scale (default 1.5) before applying the sigmoid, and clips the scaled score to [-8, 8] for numerical stability. The v0.2.1 reference formula uses an implicit scale of 1.0 and no clipping. The temperature factor is necessary because robust_zscore (MAD-based) typically produces smaller absolute values than standard z-scores; without scaling, all G_f values cluster near g_floor + 0.5 * (1 - g_floor), making the weighted stack nearly unweighted. The clipping is a safety net that is never active in practice because individual z-scores are already clamped to [-5, 5], but it prevents exp overflow on extreme inputs.

The weights w_sharp, w_snr, w_background are configured directly as g_w_sharp, g_w_snr, g_w_background_penalty. At runtime they are converted to effective weights w_*_eff:

  • If a configured weight is <= 0, its effective weight is 0.
  • If fewer than three finite positive summary values are available, the effective weight is 0.
  • If the coefficient of variation CV = MAD / median of the finite positive summary values is below 0.01, the effective weight is 0. This prevents near-constant signals from amplifying noise and inverting the quality ranking.

The remaining effective weights are renormalised so that:

w_sharp_norm + w_snr_norm + w_background_norm = 1

if at least one effective weight is positive. If all effective weights are zero, every frame receives G_f = g_floor.

Normative defaults (v0.2.1):

The v0.2.1 reference defaults are:

  • g_floor = 0.05
  • g_w_sharp = 0.6
  • g_w_snr = 0.4
  • g_w_background_penalty = 0.3

The current operating defaults (post-v0.2.1 revision) are:

  • g_floor = 0.03
  • g_w_sharp = 0.55
  • g_w_snr = 0.30
  • g_w_background_penalty = 0.25

These were tuned empirically: the lower floor and more balanced weights prevent a small number of high-quality frames from dominating the stack on typical deep-sky datasets where frame-to-frame quality variation is moderate.

Post-v0.2.1 extension default:

  • g_k_scale = 1.5 (sigmoid temperature; 1.0 restores the v0.2.1 reference formula)

Setting g_w_background_penalty = 0.0 restores the exact v0.2.0 global quality definition.

Rationale. A strong large-scale gradient means that the background model used by the SNR signal (b_s in §2.3.2(b)) is a biased local estimate. Frames with very flat backgrounds tend to be cleaner and more linear; frames with a strong moon-glow or light-pollution gradient receive a lower global weight, reducing their influence on the final stack without removing them entirely.

Compatibility note. The background penalty is not derived from Q_map. It is therefore an extension of v0.2.0, not a contradiction. It must be clearly reported in aqmh_metrics.json as the per-frame field global_background_penalty_input, with source global_background_penalty_source: "sky_gradient". The configured penalty weight is part of the AQMH global-quality configuration, not the registration_weight_guard artifact.

2. Quality Map Computation

2.1 Overview

Identical to v0.2.0. AQMH computes a dense quality map for each frame/channel pair by fusing multi-scale local sharpness, SNR and artifact-anomaly signals.

2.2 Shared Preprocessing

Identical to v0.2.0. All frames must be calibrated, registered and prewarped to a common output canvas before AQMH map computation.

2.3 Multi-Scale Pyramid

Identical to v0.2.0 §2.3. The four scales, omission rule, sharpness, SNR and artifact computations, and the geometric-mean fusion are unchanged.

2.4 Multi-Scale Fusion

Identical to v0.2.0 §2.4.

Q_map_{f,c}(x,y) = ( prod_{s in S_actual} Psi_s^{up}(x,y) )^{1/P_actual}

implemented as exp(mean_s(log(Psi_s^{up}))) with the exact-zero veto and output guard.

2.5 Block-Level Diagnostic Summaries

Identical to v0.2.0 §2.5.

3. Quality Map Storage and Memory Model

The default storage mode is full-resolution float32 with resolution_divisor = 1. An optional performance mode uses uint16 with resolution_divisor = 2 for reduced memory footprint; this is not the default and must be explicitly reported. Cherry-pick requires the reference mode because a reduced or quantised map can change the per-pixel ranking. Each run must report resolution and data type.

The background-penalty signal does not affect quality-map storage; it is a per-frame scalar computed during or after map computation and stored in aqmh_metrics.json.

4. Pipeline Integration

4.1 AQMH Processing Stages

Identical to v0.2.0:

AQMH_MAPS
AQMH_GLOBAL_QUALITY
AQMH_RECONSTRUCTION
AQMH_DIAGNOSTICS
AQMH_NATIVE_BGE_INPUTS

The output of AQMH_RECONSTRUCTION is additionally persisted unchanged as outputs/aqmh_reconstructed_raw.fit. For OSC data this artifact still contains the CFA pattern and is the only valid input for a resume from STACKING. reconstructed_L.fit is not a resume artifact: STACKING replaces it with the scaled luminance output. If an older run lacks the raw artifact, the runner must rerun AQMH_RECONSTRUCTION from the map and prewarp caches. Already stacked luminance must never be debayered again as CFA data. Set aqmh.reconstruction.delete_prewarped_cache_after_run: false to retain the cache/prewarped_frames directory for later resumes; the default true continues to reclaim the disk space after the run.

4.2 Global Quality Stage (v0.2.1 update)

The stage now computes, for each frame, the three summary vectors g_sharp, g_snr, g_background and passes them to compute_aqmh_global_quality. The result is a vector G_f per frame.

All three inputs are recorded per frame in aqmh_metrics.json:

  • global_sharpness_input
  • global_sharpness_source: "laplacian_variance" or "psf_wfwhm_inverted" (post-v0.2.1 extension)
  • global_snr_input
  • global_background_penalty_input
  • global_background_penalty_source: "sky_gradient"
  • global_quality_input_invalid
  • global_quality (the final G_f)

When the PSF-FWHM sharpness proxy is used, global_sharpness_input already contains the 1 / wfwhm value.

4.3 Registration-Weight Guard (v0.2.1 addition)

Before reconstruction, the runner may optionally apply a registration-weight guard to G_f. It reads the shared global_registration.json artifact, which must contain per-frame fields cc (cross-correlation confidence), source (registration source type) and optionally chain_depth.

For each frame f:

  1. Cross-correlation mapping. Direct and reference solutions are not continuously damped above the floor:
r_cc = cc_f >= cc_floor ? 1.0 : r_floor

Sequential, predicted, interpolated, and unknown solutions use:

t = clamp( (cc_f - cc_floor) / (cc_full - cc_floor), 0, 1 )
r_cc = r_floor + (1 - r_floor) * t

with defaults r_floor = 0.30, cc_floor = 0.35, cc_full = 0.80.

  1. Registration-source damping.

  2. If source == "sequential_refined": r_f *= sequential_factor (default 0.92).

  3. If source contains "predicted", "interpolated", or is "unknown": r_f *= predicted_factor (default 0.50).

  4. Chain-depth damping for non-direct solutions.

depth_penalty = min( depth_max, max(0, depth_f - 1) * depth_penalty_per_step )
r_f *= (1 - depth_penalty)

with defaults depth_penalty_per_step = 0.03, depth_max = 0.15.

  1. Clamp.
R_f = clamp(r_f, r_floor, 1.0)

The effective global weight used in reconstruction is:

G_f^{eff} = G_f * R_f

The guard is enabled by default (registration_weight_guard: true) and reported in aqmh_reconstruction.json under registration_weight_guard.

Rationale. Deep chain-predicted or weakly-correlated frames can survive eligibility filtering but still carry lower registration accuracy. The guard prevents high AQMH quality scores from amplifying registration errors. It is a shared-infrastructure multiplier and is therefore documented as a robustness extension, not as part of the core AQMH quality model.

4.4 Registration NCC preprocessing (v0.2.1 addition)

Before registration NCC comparisons, the normalized proxy images are prepared for robust correlation as follows:

  1. Clamp the proxy image to nonnegative values to remove negative values caused by background subtraction.
  2. Apply a Gaussian blur with sigma = 1.5 px to reduce the influence of hot pixels and isolated defects.
  3. Compute both identity-overlap NCC and warped-overlap NCC from these prepared images.

A near-identity result is accepted only when all of the following hold:

  • total shift is smaller than star_inlier_tol_px;
  • absolute rotation is below 0.1°;
  • warped NCC is no more than 0.02 below identity-overlap NCC; and
  • identity-overlap NCC is greater than 0.7.

The identity-NCC condition is essential: a near-zero warp with low correlation must not be accepted merely because the optimizer found no meaningful shift. This registration fix is upstream of AQMH and does not alter Q_map; it improves the reliability of the cc, source, and chain_depth metadata used by the registration-weight guard.

5. Pixel-Wise Weighted Reconstruction

5.1 Reconstruction Formula

Identical to v0.2.0. For each output channel:

R(p) = sum_{f in V_c^I(p)} w_f(p) * I_f(p) / sum_{f in V_c^I(p)} w_f(p)

where w_f(p) = G_f^{eff} * Q_map_{f,c}(p) and V_c^I(p) is the set of frames with finite intensity and finite quality-map value at pixel p.

The geometric support of each registered frame is part of V_c^I(p). Prewarp pixels outside that support must remain invalid (NaN plus the per-frame support mask); zero-filled warp borders must never enter AQMH as real intensity samples. Three mask roles remain separate:

  • The frame-support mask states which pixels are supplied by one frame.
  • The common-overlap mask is used only for analysis, validation, and calibration at the configured minimum coverage.
  • The output mask is the union of all frame-support masks and preserves every genuinely reconstructable edge structure.

The common-overlap mask must not crop AQMH reconstruction or BGE, PCC, and HMS outputs to the common core. Pixels that do not satisfy min_n_eff remain diagnosable as insufficiently supported, but they must not cause valid nearby pixels from a few frames to be diluted by nonexistent zero samples.

5.2 Sigma Clipping and Effective-Sample Sufficiency

Identical to v0.2.0. Iterative sigma clipping with clip_sigma_low and clip_sigma_high, and a minimum effective sample count min_n_eff and minimum fraction min_fraction.

5.3 Cherry-Pick Stacking Mode

Identical to v0.2.0 §5.3. The run-level K_nominal_median floor, per-pixel K(p) = max(k_min_required, K_nominal(p)) rule, tiering and rank-separation diagnostics are unchanged.

6. Post-Reconstruction Robustness Extensions (v0.2.1)

6.1 Uniform Control Mean

When compute_uniform_control: true, the reconstruction routine also computes the unweighted mean of the registered frames over the same valid-pixel set. This mean is called the uniform-control output U(p):

U(p) = sum_{f in V_c^I(p)} I_f(p) / |V_c^I(p)|

U(p) is not a quality-weighted result; it is a diagnostic reference.

6.2 Validation Metrics

Both the raw AQMH output A(p) and any post-processed candidate are compared to U(p) using the same metrics as v0.2.0 validation:

  • seam_score_regression
  • fwhm_regression
  • background_rms_regression
  • tail11_abs_regression
  • elongation_regression

Here, background_rms is not the global intensity spread of the image. It is estimated robustly from horizontal and vertical pixel differences (1.4826 * MAD(diff / sqrt(2))). Slowly varying nebula, galaxy, and IFN signal is therefore not classified as background noise.

These comparisons are recorded in aqmh_reconstruction.json. Each metric must also record an applicability state:

status = pass | fail | not_applicable

not_applicable is required when either side of the comparison is missing, non-finite, has too few samples, or would require a relative regression against a zero/near-zero control denominator. A not_applicable metric is diagnostic only and must not by itself trigger fallback to uniform control.

6.3 Adaptive Low-Frequency Neutralisation

If the uniform control U(p) is available, an optional neutralised candidate N(p) is computed:

L(p) = GaussianBlur( A(p) - U(p), sigma = 96 px )
N(p) = A(p) - L(p)

The blur uses a reflect-101 border mode. The sigma of 96 px was chosen empirically to target large-scale "veil" residuals without affecting structure on smaller scales.

A validation comparison compare(N, U) is computed. N(p) may be selected as the base over A(p) only when the background RMS metric is applicable and its regression is strictly smaller:

background_rms_regression(N, U) < background_rms_regression(A, U)

If the raw AQMH candidate already passes applicable background gates, the neutralised candidate must not replace it unless it also preserves the primary image-quality metrics used by the final selector. The configured background threshold is recorded as a diagnostic gate at this stage; the final structure candidate and final output are subject to the applicable validation gates in §6.4 and §6.5. The selected base image is called B(p) (either A(p) or N(p)).

Rationale. The per-pixel weighted mean can, in rare cases, create a low-frequency residual that is smoother than the true background. Subtracting the blurred difference to the unweighted mean removes this additive low-frequency component while preserving higher-frequency detail.

6.4 Structure-Masked Detail Blending

After selecting the base B(p), a second optional candidate tries to preserve AQMH detail in high-structure regions while keeping the smoother background from B(p):

  1. Compute the gradient magnitude grad(U) of the uniform-control mean.
  2. Build a soft structure mask M_s(p) by mapping the gradient magnitude from the low_q = 0.40 quantile to the high_q = 0.90 quantile to [0, 1] and then Gaussian-blurring with sigma = 4 px. The v0.2.1 reference values were low_q = 0.70, high_q = 0.97, sigma = 2 px; the current operating defaults were widened to preserve mid-gradient structure (spiral arms, dust lanes) that the original narrow range suppressed.
  3. Compute the detail candidate:
D(p) = U(p) + M_s(p) * (B(p) - U(p))

In high-structure regions (M_s ≈ 1) D(p) follows the AQMH base; in smooth regions (M_s ≈ 0) it follows the uniform control.

The structure mask is a scene-independent signal-confidence estimate, not a nebula-specific heuristic. Implementations may extend it with additional deterministic multi-scale structure measures (for example DoG/Laplacian or background-mask-aware faint-structure confidence), provided that all components are reported and no object-specific rules are used. This is important for galaxies, where scientifically relevant spiral arms and dust lanes often occupy mid-gradient percentile ranges rather than only the top gradient quantiles.

D(p) is accepted if it passes all applicable validation thresholds:

background_rms_regression(D, U) <= max_background_rms_regression
fwhm_regression(D, U)            <= max_fwhm_regression
seam_score_regression(D, U)      <= max_seam_score_regression
tail11_abs_regression(D, U)      <= max_tail11_abs_regression
elongation_regression(D, U)      <= max_elongation_regression

and it improves at least one of FWHM or seam score relative to U.

If D(p) fails, an alpha-blended attenuation search is performed over alpha ∈ [0, 1]:

D_alpha(p) = U(p) + alpha * M_s(p) * (B(p) - U(p))

The largest alpha that satisfies the applicable validation thresholds and improves FWHM or seam score is selected. If no alpha > 0 passes, the base B(p) is kept.

6.5 Final Protection Gate

After all post-processing, the selected output O(p) is validated one more time against U(p) and the immutable raw AQMH baseline A(p). If:

background_rms_regression(O, U) > max_background_rms_regression

or any other applicable configured threshold is exceeded, the runner rejects the post-processed candidate and emits A(p). U(p) remains a diagnostic reference only. Blending toward U(p) is forbidden because it can erase faint diffuse signal while one-sided noise metrics appear to improve.

6.6 Reporting Requirements

aqmh_reconstruction.json must contain:

  • low_frequency_neutralization_applied (true/false)
  • low_frequency_neutralization (comparison metrics plus sigma_px)
  • structure_masked_detail_applied (true/false)
  • structure_masked_detail_alpha (final blend alpha if attenuation was used)
  • structure_masked_detail_validation
  • uniform_control_gate_triggered (true/false)
  • raw_aqmh_validation
  • final_vs_raw_aqmh_validation
  • raw_aqmh_preserved_by_guard (true/false)
  • selected_candidate

7. Validation

7.1 Regression Validation Against Uniform Control

Identical to v0.2.0 §9. The reconstructed output is compared to the uniform-control mean. Regression thresholds:

Current operating defaults (post-v0.2.1 revision):

  • max_seam_score_regression = 0.05
  • max_fwhm_regression = 0.02
  • max_background_rms_regression = 0.05
  • max_tail11_abs_regression = 0.10
  • max_elongation_regression = 0.08

The v0.2.1 reference values were 0.02 for seam/FWHM/background and 0.05 for tail/elongation. The current defaults are wider for seam, background, tail, and elongation to reduce false rejections on real-world datasets where sub-threshold regressions are common and do not indicate a meaningful quality degradation.

These thresholds apply only to metrics whose applicability state is pass or fail. Metrics reported as not_applicable are excluded from the hard veto and must carry a reason string in the diagnostic artifact.

7.2 Zero-Veto Test

Identical to v0.2.0. When all weights are zero, the output must be zero, not an unweighted mean.

7.3 No Structural Injection

Identical to v0.2.0. The AQMH output must not introduce structure that exceeds the uniform-control output by the configured regression thresholds.

8. Diagnostics

Identical to v0.2.0 §6 and §7, with the addition of the fields listed in §6.6.

Per-frame diagnostics in aqmh_metrics.json include:

  • map_mean, map_p10, map_p90
  • artifact_frac
  • sharpness_p50, snr_p50
  • n_regions
  • global_quality
  • global_sharpness_input, global_snr_input
  • global_sharpness_source: "laplacian_variance" or "psf_wfwhm_inverted" (post-v0.2.1 extension)
  • global_background_penalty_input and global_background_penalty_source: "sky_gradient" (v0.2.1)
  • global_quality_input_invalid

9. Configuration Summary

9.1 Data and Pipeline

  • data.color_mode: OSC for one-shot-color data.
  • data.bayer_pattern: default auto. The FITS header values BAYERPAT and COLORTYP take precedence; a config value is used only as a fallback when the header has no Bayer metadata. This change was introduced to prevent example-config defaults from overriding camera metadata.

9.2 AQMH Core Parameters (unchanged from v0.2.0)

  • aqmh.pyramid.scales = 4
  • aqmh.pyramid.base_window_px = 4
  • aqmh.pyramid.w_sharp = 0.6
  • aqmh.pyramid.w_snr = 0.4
  • aqmh.pyramid.k_artifact = 3.0
  • aqmh.pyramid.frac_artifact_max = 0.25
  • aqmh.storage.resolution_divisor = 1
  • aqmh.storage.dtype = "float32"

9.3 Global Quality (v0.2.1)

  • aqmh.global_quality.g_floor = 0.03
  • aqmh.global_quality.g_w_sharp = 0.55
  • aqmh.global_quality.g_w_snr = 0.30
  • aqmh.global_quality.g_w_background_penalty = 0.25
  • aqmh.global_quality.g_k_scale = 1.5 (post-v0.2.1 extension; 1.0 restores the v0.2.1 reference formula)

The v0.2.1 reference defaults were g_floor=0.05, g_w_sharp=0.6, g_w_snr=0.4, g_w_background_penalty=0.3.

Set g_w_background_penalty = 0.0 to obtain the exact v0.2.0 behaviour.

9.4 Registration-Weight Guard (v0.2.1)

  • aqmh.reconstruction.registration_weight_guard = true
  • aqmh.reconstruction.registration_weight_floor = 0.30
  • aqmh.reconstruction.registration_cc_floor = 0.35
  • aqmh.reconstruction.registration_cc_full = 0.80
  • aqmh.reconstruction.registration_sequential_factor = 0.92
  • aqmh.reconstruction.registration_predicted_factor = 0.50
  • aqmh.reconstruction.registration_chain_depth_penalty = 0.03
  • aqmh.reconstruction.registration_chain_depth_max_penalty = 0.15

9.5 Neutralisation and Blending (v0.2.1)

  • Neutralisation blur sigma: 96 px (hard-coded).
  • Structure-mask quantiles: low_q = 0.40, high_q = 0.90.
  • Structure-mask blur sigma: 4 px.
  • Validation thresholds are taken from aqmh.validation.

The v0.2.1 reference values were low_q=0.70, high_q=0.97, blur sigma 2 px; the current operating defaults are wider to preserve mid-gradient structure.

9.6 Cherry-Pick (unchanged)

  • aqmh.cherry_pick.enabled = false by default.
  • k_frac = 0.30
  • k_min_required = 20
  • margin_min = 0.02

10. Conformance Statement

A run is v0.2.1-conformant if and only if:

  1. It follows all binding invariants of v0.2.0 (§1.3).
  2. It computes Q_map according to §2 and §3 with full-resolution float32 storage unless an explicitly approximate mode is selected and reported.
  3. It computes global quality using the extended formula of §1.5 when g_w_background_penalty > 0, or using the v0.2.0 formula when it is 0.
  4. It applies the registration-weight guard as described in §4.3 when enabled, and reports the result.
  5. It performs post-reconstruction validation and optional neutralisation as described in §6, and records the selected candidate and any fallback.
  6. It produces aqmh_metrics.json, aqmh_reconstruction.json and all required diagnostic fields.

A run is strict v0.2.0-conformant if g_w_background_penalty = 0, registration_weight_guard = false, and all post-reconstruction extensions are disabled. Such a run is a valid subset of v0.2.1.

11. References

  • aqmh_methodik_en_v0.2.0.md — baseline methodology.
  • tile_compile_cpp/include/tile_compile/config/configuration.hpp — configuration structs.
  • tile_compile_cpp/src/metrics/aqmh_global_quality.cpp — global quality computation.
  • tile_compile_cpp/apps/runner_phase_aqmh_reconstruction.cpp — registration-weight guard, neutralisation and blending.
  • tile_compile_cpp/src/metrics/aqmh_quality_map.cpp — quality-map computation.
  • tile_compile_cpp/src/reconstruction/aqmh_reconstruction.cpp — weighted reconstruction and cherry-pick logic.