Image Denoising Using Lower Semi-Frames

This paper documents the implementation and evaluation of a self-supervised denoising framework on Inertial Confinement Fusion (ICF) images corrupted by Multiplicative Uniform noise: the Log-Domain Noisier2Inverse framework. This framework is developed and analysed in this work; the key theoretical result -- that minimising the log-domain self-supervised loss is equivalent to supervised learning in the transformed domain -- is presented with full proof. We document significant implementation challenges arising from the unique characteristics of ICF imagery, describe the fixes applied at each stage, and report final quantitative results. The log-domain approach with per-image JSON Uniform noise loading (VariantB) achieves the best result: a mean PSNR of $21.41\db$ and SSIM of $0.8358$, a $+19.46\db$ improvement over the noisy input baseline of $1.95\db$, substantially outperforming BM3D log-domain ($4.47\db$, SSIM $0.5181$) and Noise2Self ($4.75\db$, SSIM $0.0177$). VariantA, using fixed Gaussian noise loading, achieves $21.39\db$ PSNR and SSIM $0.8436$. Of the three evaluated methods, Log-Domain Noisier2Inverse and Noise2Self are entirely self-supervised during training, requiring no clean ground truth data; BM3D is a classical filter-based method requiring no training at all. The clean reference images are used solely for quantitative evaluation of all three methods.

Classical training-free denoisers such as BM3D and non-local means owe much of their strength to search: content-dependent block matching whose memory traffic and data-dependent control flow parallelize poorly and preclude fixed-latency implementations. Learned denoisers reach the highest quality, but they need training data, degrade outside their training domain (which we also observe), and carry per-pixel compute budgets that effectively require a GPU. We present GALOSH (Generalized Anscombe LOcal SHrinkage), a redesign of training-free denoising that removes the search entirely and aims at multi-domain coverage, speed, and quality at once: a blind per-image Poisson-Gaussian noise fit, a generalized Anscombe transform, a two-pass local Walsh-Hadamard shrinkage of luminance, and a luminance-guided local regression of chrominance -- two deliberately different operators for the two perceptually different noise components, each with its own strength control. Every stage is local, data-independent, and regular -- the same computation graph for every pixel of every image. One core serves two domains: raw Bayer mosaics and sRGB/YUV images. On four real-noise benchmarks (SIDD Medium and RawNIND, raw and sRGB) GALOSH is consistently the strongest among the tested blind, training-free methods -- surpassing BM3D- and NLM-family baselines even when those are given an oracle noise level -- and approaches trained networks on raw data while remaining below in-domain trained networks at high ISO in sRGB. Being search-free makes it fast: 7x-650x faster than the DL baselines on the same GPU at full benchmark size, and the only strong method in the comparison that also runs practically on plain CPUs. The fixed, data-independent structure is designed to map naturally onto fixed-point and streaming hardware, supported by an operation-count analysis and a working INT16 fixed-point realization.

Low-count imaging arises when limited illumination or dose yields only a few detected particles in microscopy, such as photons or electrons, causing measurements to be dominated by signal-dependent Poisson shot noise. Supervised denoisers typically require paired clean and noisy observations, whereas many self-supervised approaches exploit spatial or temporal redundancy without directly estimating the underlying particle-arrival process. We introduce PARM, a self-supervised denoising framework based on particle-arrival-rate matching. By modeling particle accumulation over exposure as a Poisson counting process, PARM identifies the conditional particle-arrival-rate field with the posterior mean of the latent clean rate. Poisson thinning then splits each observation into complementary lower-exposure views that provide self-supervised rate targets for one another. In implementation, the network estimates the normalized spatial allocation of the conditional rate, while the observed total count determines its global particle mass. Experiments on synthetic data, natural-video sequences corrupted with Poisson noise, and real low-dose electron microscopy demonstrate leading or competitive performance while effectively preserving fine structures. PARM therefore provides a statistically grounded approach to low-count image denoising when clean references are unavailable.