Self-supervised image denoising methods have traditionally relied on either architectural constraints or specialized loss functions that require prior knowledge of the noise distribution to avoid the trivial identity mapping. Among these, approaches such as Noisier2Noise or Recorrupted2Recorrupted, create training pairs by adding synthetic noise to the noisy images. While effective, these recorruption-based approaches require precise knowledge of the noise distribution, which is often not available. We present Learning to Recorrupt (L2R), a noise distribution-agnostic denoising technique that eliminates the need for knowledge of the noise distribution. Our method introduces a learnable monotonic neural network that learns the recorruption process through a min-max saddle-point objective. The proposed method achieves state-of-the-art performance across unconventional and heavy-tailed noise distributions, such as log-gamma, Laplace, and spatially correlated noise, as well as signal-dependent noise models such as Poisson-Gaussian noise.

We propose ODER as a new strategy for improving the efficiency of DEQ through stochastic approximations of the measurement models. We theoretically analyze ODER giving insights intoits ability to approximate the traditional DEQ approach for solving inverse problems.

We consider the problem of estimating a vector from its noisy measurements using a prior specified only through a denoising function. Recent work on plug-and-play priors (PnP) and regularization-by-denoising (RED) has shown the state-of-the-art performance of estimators under such priors in a range of imaging tasks. In this work, we develop a new block coordinate RED algorithm that decomposes a large-scale estimation problem into a sequence of updates over a small subset of the unknown variables. We theoretically analyze the convergence of the algorithm and discuss its relationship to the traditional proximal optimization. Our analysis complements and extends recent theoretical results for RED-based estimation methods. We numerically validate our method using several denoiser priors, including those based on convolutional neural network (CNN) denoisers.

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives provide additional local information about the data distribution and enable new applications. Although they can be estimated via automatic differentiation of a learned density model, this can amplify estimation errors and is expensive in high dimensional settings. To overcome these limitations, we propose a method to directly estimate high order derivatives (scores) of a data density from samples. We first show that denoising score matching can be interpreted as a particular case of Tweedie's formula. By leveraging Tweedie's formula on higher order moments, we generalize denoising score matching to estimate higher order derivatives. We demonstrate empirically that models trained with the proposed method can approximate second order derivatives more efficiently and accurately than via automatic differentiation. We show that our models can be used to quantify uncertainty in denoising and to improve the mixing speed of Langevin dynamics via Ozaki discretization for sampling synthetic data and natural images.

Inference in dynamic probabilistic models is a complex task involving expensive operations. In particular, for Hidden Markov Models, the whole state space has to be enumerated for advancing in time. Even states with negligible probabilities are considered, resulting in computational inefficiency and increased noise due to the propagation of unlikely probability mass. We propose to denoise the future and speed up inference by using only the top-p states, i.e., the most probable states with accumulated probability p. We show that the error introduced by using only the top-p states is bound by p and the so-called minimal mixing rate of the underlying model. Moreover, in our empirical evaluation, we show that we can expect speedups of at least an order of magnitude, while the error in terms of total variation distance is below 0.09.

Photoplethysmography (PPG) is widely used in wearable health monitoring, but its reliability is often degraded by noise and motion artifacts, limiting downstream applications such as heart rate (HR) estimation. This paper presents a deep learning framework for PPG denoising with an emphasis on preserving physiological information. In this framework, we propose DPNet, a Mamba-based denoising backbone designed for effective temporal modeling. To further enhance denoising performance, the framework also incorporates a scale-invariant signal-to-distortion ratio (SI-SDR) loss to promote waveform fidelity and an auxiliary HR predictor (HRP) that provides physiological consistency through HR-based supervision. Experiments on the BIDMC dataset show that our method achieves strong robustness against both synthetic noise and real-world motion artifacts, outperforming conventional filtering and existing neural models. Our method can effectively restore PPG signals while maintaining HR accuracy, highlighting the complementary roles of SI-SDR loss and HR-guided supervision. These results demonstrate the potential of our approach for practical deployment in wearable healthcare systems.

Denoising is a core operation in modern video pipelines. In codecs, in-loop filters suppress sensor noise and quantisation artefacts to improve rate-distortion performance; in cinema post-production, denoisers are used for restoration, grain management, and plate clean-up. However, state-of-the-art deep denoisers are computationally intensive and, at scale, are typically deployed on GPUs, incurring high power and cost for real-time, high-resolution streams. This paper presents Real-Time Denoise (ReTiDe), a hardware-accelerated denoising system that serves inference on data-centre Field Programmable Gate Arrays (FPGAs). A compact convolutional model is quantised (post-training quantisation plus quantisation-aware fine-tuning) to INT8 and compiled for AMD Deep Learning Processor Unit (DPU)-based FPGAs. A client-server integration offloads computation from the host CPU/GPU to a networked FPGA service, while remaining callable from existing workflows, e.g., NUKE, without disrupting artist tooling. On representative benchmarks, ReTiDe delivers 37.71$\times$ Giga Operations Per Second (GOPS) throughput and 5.29$\times$ higher energy efficiency than prior FPGA denoising accelerators, with negligible degradation in Peak Signal-to-Noise Ratio (PSNR)/Structural Similarity Index (SSIM). These results indicate that specialised accelerators can provide practical, scalable denoising for both encoding pipelines and post-production, reducing energy per frame without sacrificing quality or workflow compatibility. Code is available at https://github.com/RCSL-TCD/ReTiDe.