SEM Noise Profile

Technical description

M6 is a deterministic, generator-agnostic screen for the spatial noise profile of electron microscopy. Electron imaging is a counting process, so a genuine micrograph always carries shot noise, and because the beam scans the whole frame with the same dwell time and detector, that noise is present everywhere at a roughly constant level. Fabrication breaks this in recognizable ways: a collage stitched from separate captures has regions whose noise levels differ, a synthetic or aggressively denoised image has almost no noise at all, and either can present a signal-to-noise ratio higher than any real acquisition at useful magnification. M6 extracts a noise residual by subtracting a median-filtered copy of the image, estimates the noise level robustly on a grid of blocks, and reads the spatial variation of that level, the global level, and the resulting signal-to-noise ratio. The image must be at least 64 by 64 pixels, or the indicator returns a zero score and records that it was skipped.

How it works

The grayscale image is filtered with a 5 by 5 median filter, which follows the specimen structure, and the residual r = image - median(image) isolates the high-frequency content where sensor noise dominates. The noise level of each region is estimated with the robust median absolute deviation rather than the standard deviation:

sigma = 1.4826 * median(|r - median(r)|),

so that the strong residual values left by a specimen edge, which the median filter cannot fully follow, do not inflate the estimate. This robust level is computed both globally and on each 16 by 16 block.

Three signals drive the score. The spatial consistency is the coefficient of variation of the per-block noise levels, CV = std(levels) / mean(levels). A CV below 0.3 is consistent with a single uniform scan and scores nothing; from 0.3 to 0.7 the contribution rises linearly to 3.0, because a region stitched in from another source carries its own noise level. The absent-noise check adds 3.0 when the global noise level falls below 2.0, the signature of an image with no sensor noise. The signal-to-noise check, SNR = mean_intensity / global_noise_level, adds up to 2.0 once the ratio exceeds 50, because a real electron image at useful magnification always carries some shot noise. The contributions are summed and capped at 5.0. Findings report a suspiciously smooth image, spatially inconsistent noise, an abnormally high SNR, and individual blocks whose noise level departs from the mean by more than two standard deviations, each with its bounding box. The metadata records the noise CV, the global noise level, the SNR, the mean block level, and the block count.

Score thresholds

Score	Meaning
0 to 1	Noise is present and spatially uniform, consistent with a single electron-microscopy scan.
2 to 3	One anomaly: a noise level that varies across the frame, or an unusually high signal-to-noise ratio.
4 to 5	Noise is nearly absent, or strongly inconsistent across regions. Consistent with a synthetic image or a composite of different sources.

Why this matters

Electron microscopy is shot-noise-limited: the signal is built from counted electrons, so every real micrograph carries Poisson noise whose presence and spatial uniformity are physical facts of the instrument, and the contrast-to-noise ratio is the accepted measure of electron-image quality precisely because the noise cannot be wished away [2]. That regularity is strong enough that the shot-noise parameters can be recovered from a single SEM image, which both confirms the noise model and provides the basis for estimating its level blindly, as M6 does [1]. The forensic value follows directly: a region spliced from another capture brings a different noise level, the cue that blind noise-inconsistency forensics exploits to expose splices without a reference [3], and a synthetic or denoised region brings too little noise. M6 estimates the level with the robust median-absolute-deviation rule, the edge-resistant estimator introduced by Donoho and Johnstone, so that the specimen's own structure is not mistaken for noise [4]. By reading presence, uniformity, and ratio together, M6 turns the unavoidable shot noise of electron imaging into a test of whether a frame was acquired on one instrument in one scan.

Limitations

The median-residual estimate is robust but not perfect: very fine, pervasive texture can still raise the apparent noise level, and a low-magnification image with large flat regions can read as suspiciously smooth without manipulation. Real acquisitions vary their dwell time, detector gain, and frame averaging, all of which change the noise level legitimately, so a genuinely low-noise image, such as a frame-averaged acquisition, can trip the absent-noise or high-SNR checks. The SNR is defined from the mean intensity over the noise level, a coarse proxy that depends on the brightness of the field. The 16-pixel block bounds the spatial resolution, so a small inserted region is averaged with its surroundings. The thresholds are directional rather than exact. Whether the noise level scales with intensity, the photon-transfer question, is handled by indicator M5, and the general wavelet-domain noise-consistency screen for any image is indicator I3; M6 specialises in the spatial noise profile of electron microscopy, including the absence-of-noise and high-SNR signatures that I3 does not score, so the three corroborate each other.

Theoretical background

M6 rests on the counting statistics of electron imaging. In a scanning electron microscope the beam dwells on each pixel and the detector counts secondary or backscattered electrons; the count is a Poisson variable, so noise is intrinsic to the measurement and its level is set by the dwell time, the beam current, and the detector, all of which are constant across a single raster scan. The result is a frame whose noise is everywhere present and everywhere at the same level, a spatial regularity that is a fingerprint of the acquisition rather than of the specimen. A composite assembled from different captures cannot preserve that regularity, because each source was acquired with its own settings, and a synthetic image rendered without a detector carries no shot noise at all. Subtracting a median-filtered copy removes the specimen structure and leaves the noise, and the robust median-absolute-deviation level reads that noise while ignoring the residual edges that structure leaves behind. Reading the spatial uniformity, the presence, and the ratio of that noise tests the image against the physics of how an electron micrograph is formed.

References

1. Kockentiedt S, Tönnies K, Gierke E, Dziurowitz N, Thim C, Plitzko S. Poisson shot noise parameter estimation from a single scanning electron microscopy image. Proceedings of SPIE 8655, Image Processing: Algorithms and Systems XI. 2013:86550N. DOI: 10.1117/12.2008374
2. Timischl F. The contrast-to-noise ratio for image quality evaluation in scanning electron microscopy. Scanning. 2015;37(1):54-62. DOI: 10.1002/sca.21179
3. Mahdian B, Saic S. Using noise inconsistencies for blind image forensics. Image and Vision Computing. 2009;27(10):1497-1503. DOI: 10.1016/j.imavis.2009.02.001
4. Donoho DL, Johnstone IM. Ideal spatial adaptation by wavelet shrinkage. Biometrika. 1994;81(3):425-455. DOI: 10.1093/biomet/81.3.425