ARTS2D: use a noise-aware, regularized objective with explicit gain nuisances

[joglekara]

Problem

The limited-angle ARTS2D inverse objective is currently neither statistically weighted nor regularized, and it uses nonsmooth peak normalization that can let one resonant pixel rescale an entire angular trace.

Concrete issues:

• tsadar/inverse/loss_function.py:388 hard-codes penalty_error = 0.0, so configured EDF/moment penalties never enter the loss.
• The existing 2-D moment penalty exponentiates an already-positive physical EDF and contains incomplete/incompatible 2-D moment calculations.
• The angular L2 objective divides squared residuals by one global amplitude scalar rather than a per-pixel variance; noiseE is not used to whiten the residual.
• tsadar/core/thomson_diagnostic.py:183 scales every model row to the measured row maximum. amax is noisy and nonsmooth when the argmax switches, discards absolute angular-amplitude information, and couples a single unresolved spike to all wavelengths in the row.
• The angular IRF also restores peaks; the physical convolution issue is tracked separately.

Proposed direction

• Use a documented detector likelihood, initially Poisson plus read/background-subtraction noise or a justified measured covariance.
• Replace measured-maximum normalization with explicit row/wing gain nuisance parameters. For Gaussian residuals, profile linear gains analytically (variable projection) and apply smooth calibration priors across angle.
• Impose positivity by construction and regularize the physical EDF with radial/angular smoothness, entropy/KL to a baseline, and selected moment priors.
• Choose regularization strength using held-out angles/pixels, simulation calibration, discrepancy principle, or evidence—not training loss alone.

Acceptance criteria

• Configured regularizers are either applied and logged term-by-term or rejected explicitly; no silent no-op settings.
• Residuals are whitened by the documented detector noise/covariance model, and whitened residual diagnostics are persisted.
• Remove data-dependent amax scaling from the differentiable forward model; profile or fit amplitude nuisances with documented priors/identifiability constraints.
• Add bad-pixel masks and a documented robust-contamination option if needed.
• On calibrated synthetic data, recovered parameters have sensible uncertainty/coverage and are invariant to arbitrary overall intensity scaling when gain is nuisance.
• Regularization and gain treatment are tested jointly with the grid-converged, area-preserving IRF work.

Related: #124 and the separate unresolved-resonance issue.