Trainable Nonexpansive Denoisers for Contractive Image Reconstruction

Pretrained deep denoisers can be used to solve a wide range of model-based image reconstruction tasks via Plug-and-Play (PnP) and Regularization-by-Denoising (RED) algorithms, without retraining per task. These denoisers are trained only for single-step denoising. Using them as Image Reconstruction (IR) regularizers in an iterative process can destabilize reconstruction. A common failure mode is the peak-and-collapse behaviour: metrics such as PSNR improve for early iterations and then abruptly degrade, making these algorithms unreliable in practice. We propose a data-driven stabilization framework that (i) formalizes this instability of any IR operator through a local quantity and (ii) prevents collapse by regularizing this quantity adaptively, requiring no retraining or modification of the given pretrained network. Our key idea is to control the potentially unstable IR operator with a contractive operator whose stable iterates act as an anchor and prevent collapse. We further introduce an efficient family of trainable contractive operators that serve as strong anchors while remaining lightweight. Extensive experiments across proximal algorithms, denoiser architectures, noise levels, and imaging tasks show consistent, collapse-free performance and improved reliability of PnP and RED reconstruction.

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.

Image restoration faces a fundamental tradeoff: methods that minimize error produce blurry reconstructions, while those that maximize perceptual quality yield sharp but less faithful images. Existing approaches either commit to a single operating point on this distortion perception (DP) frontier or require paired-data supervision, auxiliary models, or hyperparameter tuning of the sampler to access different points. We show that flow map models, a recent extension of flow matching for few-step sampling that learns an average field, implicitly define a one-parameter family of denoisers that continuously spans the DP frontier. The lookahead parameter t acts as a control knob between the MMSE and perceptual regimes. For Gaussian targets, we prove that varying t exactly recovers the optimal DP frontier; for natural images, we observe similar behavior empirically. Within a Plug-and-Play solver, the same mechanism extends to general inverse problems, where it controls a tradeoff between perceptual alignment and data consistency. Despite the lack of exact optimality guarantees in this setting, a single trained flow map spans the DP tradeoff, matching or exceeding specialized baselines at both extremes. Extensive experiments on CelebA ($128\times 128$) and AFHQ ($256\times 256$) across several linear and nonlinear inverse tasks validate our findings.