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A partially identified model, where the parameters can not be uniquely identified, often arises during statistical analysis. While researchers frequently use Bayesian inference to analyze the models, when Bayesian inference with an…
Traditional patch-based sparse representation modeling of natural images usually suffer from two problems. First, it has to solve a large-scale optimization problem with high computational complexity in dictionary learning. Second, each…
Objective measures of image quality generally operate by comparing pixels of a "degraded" image to those of the original. Relative to human observers, these measures are overly sensitive to resampling of texture regions (e.g., replacing one…
Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. While posterior sampling is valuable for capturing uncertainty and multi-modality, many classical and practical…
Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of numerical simulations that involve complex domains. By locally improving the approximation quality we can solve expensive…
With the development of Deep Neural Networks (DNNs), plenty of methods based on DNNs have been proposed for Single Image Super-Resolution (SISR). However, existing methods mostly train the DNNs on uniformly sampled LR-HR patch pairs, which…
In recent years, it has become popular to tackle image restoration tasks with a single pretrained diffusion model (DM) and data-fidelity guidance, instead of training a dedicated deep neural network per task. However, such "zero-shot"…
This paper investigates a novel a-posteriori variance reduction approach in Monte Carlo image synthesis. Unlike most established methods based on lateral filtering in the image space, our proposition is to produce the best possible estimate…
Image processing on surfaces has drawn significant interest in recent years, particularly in the context of denoising. Salt-and-pepper noise is a special type of noise which randomly sets a portion of the image pixels to the minimum or…
Existing self-supervised learning methods based on contrastive learning and masked image modeling have demonstrated impressive performances. However, current masked image modeling methods are mainly utilized in natural images, and their…
In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…
Deep learning approaches have shown promising performance for compressed sensing-based Magnetic Resonance Imaging. While deep neural networks trained with mean squared error (MSE) loss functions can achieve high peak signal to noise ratio,…
Despite the popularity and empirical success of patch-based nearest-neighbor and weighted majority voting approaches to medical image segmentation, there has been no theoretical development on when, why, and how well these nonparametric…
Sensor placement plays a crucial role in graph signal recovery in underdetermined systems. In this paper, we present the graph-filtered regularized maximum likelihood (GFR-ML) estimator of graph signals, which integrates general graph…
When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal's non-zero coefficients can have a profound effect on recovery mean-squared error (MSE). If this distribution was apriori known, then…
The Non-Local Means (NLM) image denoising algorithm pushed the limits of denoising. But it introduced a new paradigm, according to which one could capture the similarity of images with the NLM weights. We show that, contrary to the…
We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a…
Learning a metric of natural image patches is an important tool for analyzing images. An efficient means is to train a deep network to map an image patch to a vector space, in which the Euclidean distance reflects patch similarity. Previous…
State-of-the-art algorithms for imaging inverse problems (namely deblurring and reconstruction) are typically iterative, involving a denoising operation as one of its steps. Using a state-of-the-art denoising method in this context is not…
In this paper, a novel method to adaptively approximate the solution to stochastic differential equations, which is based on compressive sampling and sparse recovery, is introduced. The proposed method consider the problem of sparse…