Image Denoising via the Adaptive Rank-Cluster Filter

Real-world video denoising for communication systems must handle mixed degradations such as sensor noise, compression artifacts, and motion-induced inconsistency while remaining deployable under tight latency budgets. Purely deep models often achieve high accuracy but come with significant computational cost, whereas classical filters are robust and efficient but insufficiently adaptive. We present FilterFusion, a prior-guided multi-frame denoising framework that combines temporally-aware learned features with an interpretable bank of denoising branches. The model predicts a low-cost guidance signal and uses it to adaptively mix a compact set of denoising responses at the original resolution. The lightweight design uses only 109K parameters and explicitly injects temporal variance and spatial variance cues into the low-resolution controller. On CRVD (real sensor noise), it reaches 34.72 dB PSNR and 0.9330 SSIM with only 0.18 GFLOPs (network-only). Because the filter-bank operations are simple and regular (Gaussian blur, median, weighted sum), a straightforward compiled C implementation of the synthesis path achieves 17.9ms per frame (55.9 FPS) on a single CPU thread at 1080p---exceeding real-time and 122--252 times faster than lightweight CNN baselines that require over 2 seconds per frame. The results demonstrate a strong quality-efficiency-speed trade-off and a practical route to real-time denoising through low-resolution control and explicit filter-based synthesis.

Gradient-based learning of morphological operators is hindered by locally sparse derivatives with respect to the structuring elements. We develop a method for learning rank filters that retains exact operator evaluation while distributing the derivatives across the window. Using threshold decomposition, we construct a neural disjunctive normal form representation and establish a sufficient condition for exactness with integer-valued images and structuring elements. We then derive a smooth surrogate from the unique root of a smooth threshold equation. Implicit differentiation gives closed-form derivatives with normalised local weights, whose distribution is controlled by a smoothing parameter. These derivatives are used in a straight-through procedure: the forward pass evaluates the exact rank filter, while the backward pass uses the surrogate. For fixed ranks, the procedure learns real-valued structuring elements of any rank filter, including the median, and extends to compositions, infima, and suprema of rank filters. Experiments on image denoising using MNIST and Fashion-MNIST and retinal vessel segmentation show that, starting from a generic random initialisation, the proposed approach consistently improves performance over training with exact subgradients in every setting. In image denoising, our best network also outperforms smooth morphological networks in all settings. On vessel segmentation, the learned erosions recover structuring elements that fit the vessels, as theoretically expected, whereas most of those trained with exact subgradients remain close to their initialisation.

The assessment of image denoising results depends on the respective application area, i.e. image compression, still-image acquisition, and medical images require entirely different behavior of the applied denoising method. In this paper we propose a novel, nonlinear diffusion scheme that is derived from a linear diffusion process in a value space determined by the application. We show that application-driven linear diffusion in the transformed space compares favorably with existing nonlinear diffusion techniques.