Small, Bias-Free, Blind and Convolutional Denoiser: A compact ConvNeXt U-Net for blind Gaussian color-image denoising

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.

Normalization Equivariance (NE) is a structural prior that improves robustness to distribution shift in image-to-image tasks. A function $f$ is normalization equivariant iff $f(a y + b\mathbf{1}) = a f(y) + b\mathbf{1}$ for all $a>0$ and $b\in\mathbb{R}$. Existing NE methods constrain every internal layer to NE-compatible operations. These constraints add runtime cost and exclude standard transformer components such as softmax attention and LayerNorm. We introduce Wrapped Normalization Equivariance (WNE), a parameter-free wrapper that normalizes the input, applies any backbone, and denormalizes the output. We prove every NE function admits this factorization, so the wrapper exactly parameterizes the class of NE functions. On blind denoising, wrapping CNN and transformer architectures improves robustness under noise-level mismatch with no measurable GPU overhead, while architectural NE baselines are up to $1.6\times$ slower.

Convolutional Neural Networks (CNNs) achieve strong denoising performance by exploiting spatial context from neighboring pixels. Deep Image Prior (DIP) leverages this property to restore images from a single noisy input without requiring large datasets. However, the over-parameterized architecture of DIP often leads to noise fitting during optimization. In this paper, we propose Pool-DIP, a convolution-free architecture that incorporates pooling-based contrast modeling to capture spatial context efficiently. Pool-DIP improves denoising performance while significantly reducing the number of parameters and computational complexity compared to convolution-based DIP models. Experimental results show that Pool-DIP achieves competitive performance across multiple datasets, including a real-world benchmark. Spectral analysis further reveals that Pool-DIP stabilizes the evolution of high-frequency components during optimization and suppresses erroneous high-frequency signals. The proposed architecture also generalizes well to other image restoration tasks such as super-resolution and inpainting.