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.

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.

Medical imaging plays a critical role in modern healthcare, enabling clinicians to accurately diagnose diseases and develop effective treatment plans. However, noise, often introduced by imaging devices, can degrade image quality, leading to misinterpretation and compromised clinical outcomes. Existing denoising approaches typically rely either on noise characteristics or on contextual information from the image. Moreover, they are commonly developed and evaluated for a single imaging modality and noise type. Motivated by Geng et.al CNCL, which integrates both noise and context, this study introduces a Dual-Pathway Learning (DPL) model architecture that effectively denoises medical images by leveraging both sources of information and fusing them to generate the final output. DPL is evaluated across multiple imaging modalities and various types of noise, demonstrating its robustness and generalizability. DPL improves PSNR by 3.35% compared to the baseline UNet when evaluated on Gaussian noise and trained across all modalities. The code is available at 10.5281/zenodo.15836053.

We examine an important setting for engineered systems in which low-power distributed sensors are each making highly noisy measurements of some unknown target function. A center wants to accurately learn this function by querying a small number of sensors, which ordinarily would be impossible due to the high noise rate. The question we address is whether local communication among sensors, together with natural best-response dynamics in an appropriately-defined game, can denoise the system without destroying the true signal and allow the center to succeed from only a small number of active queries. By using techniques from game theory and empirical processes, we prove positive (and negative) results on the denoising power of several natural dynamics. We then show experimentally that when combined with recent agnostic active learning algorithms, this process can achieve low error from very few queries, performing substantially better than active or passive learning without these denoising dynamics as well as passive learning with denoising.