The Noise Model

A parametric spectral model of EM noise — anisotropic spectrum, banding, and axial correlation — fitted to background crops of the real stack.

The components of real EM noise the model captures: colored anisotropic spectrum, banding, and between-slice correlation

The Declared Power Spectrum

The in-plane noise field is drawn from a declared power spectrum

P(k, θ) = [1 + B·|cos(θ − θ₀)|^(2p)] · k^a · exp(−(k/k_c)^b) + white

Parameter	Role
a	Spectral slope — the noise "color"
k_c, b	Cutoff frequency and rolloff shape
B, theta, p	Anisotropy: strength, orientation, angular sharpness
white	White (flat) floor
sd	Required — the noise amplitude in the tomogram's own grey units

Banding

A separate banding term (band_amp, band_ax, band_lz, band_axis) captures the stripe-like component common in tomograms. It is fitted closed-form (not search-based) by fit_banding.py — closing the 30–70% under-reproduction of real banding that the spectrum-only fit leaves behind.

Axial Correlation

Real stacks correlate between slices (measured adjacent-slice r of 0.15–0.95 across the development volumes). The zc block (zc_amp, zc_lz, plus the short-range zc2_* terms of the v4 model) makes the rendered noise planes correlate along z:

r(d) = zc_amp² · exp(−d² / (4·zc_lz²))

This term is load-bearing: the reduced "v1" model without it is rejected by the validation protocol in 27/30 cells — axial correlation is not a nicety but a property denoisers respond to.

The Contamination-Tolerant Fit

noise_fit.py fits {spectrum, banding, axial} from a background-crop stack using a difference-spectrum estimator that tolerates residual structure in the crop. Two budgets:

Budget	Settings	Time
Fast (workbench)	6 starts / maxiter 500	~2–3 min
Production	maxiter 1200	~12–19 min

The result is cached as a <crop>.noisefit.json sidecar next to the crop — instant on re-open; delete the sidecar to refit. A production-fit JSON always wins over the workbench fit.

C1: Is the Crop Clean Enough?

Fitting from a contaminated crop poisons everything downstream, so the fitter runs the C1 cleanliness checks: static z-mean excess against the fitted model, and skew/kurtosis of the marginal. The purity study behind these checks separates clean from contaminated noise sources at p < 10⁻⁵. The workbench surfaces the verdict as the C1 badge.

The Noise File

Either shape is accepted (one model per file):

// nested
{ "params": { "a": -0.5, "kc": 0.34, "b": 2.8, "B": 0.35, "theta": 15.3, "p": 1.04, "white": 1.18 },
  "band":   { "band_amp": 0.1, "band_ax": -1.0, "band_lz": 6.0, "band_axis": "y" },
  "zc":     { "zc_amp": 0.9, "zc_lz": 1.4 },
  "sd": 1.54 }

// or flat: parameters + sd at the top level; band_* / zc_* optional

zc_amp and zc_lz are scale-free, so they transfer across grey scales. Absent terms default to zero.

Related

• Tuner Workbench — fitting from a crop in the UI
• The Validation Protocol — how the model's realism is tested