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There has been tremendous research on the design of image regularizers over the years, from simple Tikhonov and Laplacian to sophisticated sparsity and CNN-based regularizers. Coupled with a model-based loss function, these are typically…

We propose a general framework to recover underlying images from noisy phaseless diffraction measurements based on the alternating directional method of multipliers and the plug-and-play technique. The algorithm consists of three-step…

A range of nonlinear image reconstruction procedures based on extremizing the generalized Shannon entropy, Kullback-Leibler cross-entropy and Renyi information measures and proposed by the author in early papers is presented. The…

Although image restoration has advanced significantly, most existing methods target only a single type of degradation. In real-world scenarios, images often contain multiple degradations simultaneously, such as rain, noise, and haze,…

Image prior modeling is the key issue in image recovery, computational imaging, compresses sensing, and other inverse problems. Recent algorithms combining multiple effective priors such as the sparse or low-rank models, have demonstrated…

Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…

We consider the imaging of cosmic strings by using Cosmic Microwave Background (CMB) data. Mathematically, we study the inversion of an X-ray transform in Lorentzian geometry, called the light ray transform. The inverse problem is highly…

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…

One key ingredient of image restoration is to define a realistic prior on clean images to complete the missing information in the observation. State-of-the-art restoration methods rely on a neural network to encode this prior. Moreover,…

We consider image denoising using a nonlinear diffusion process, where we solve unsteady partial differential equations with nonlinear coefficients. The noised image is given as an initial condition, and nonlinear coefficients are used to…

Existing image simplification techniques often rely on Non-Photorealistic Rendering (NPR), transforming photographs into stylized sketches, cartoons, or paintings. While effective at reducing visual complexity, such approaches typically…

Degradation-agnostic image restoration aims to handle diverse corruptions with one unified model, but faces fundamental challenges in balancing efficiency and performance across different degradation types. Existing approaches either…

In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…

Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…

Plug-and-play priors (PnP) is a powerful framework for regularizing imaging inverse problems by using advanced denoisers within an iterative algorithm. Recent experimental evidence suggests that PnP algorithms achieve state-of-the-art…

Accurate alignment is crucial for video denoising. However, estimating alignment in noisy environments is challenging. This paper introduces a cascading refinement video denoising method that can refine alignment and restore images…

We propose a new space-variant regularization term for variational image restoration based on the assumption that the gradient magnitudes of the target image distribute locally according to a half-Generalized Gaussian distribution. This…

Reconstruction of images corrupted by noise is an important problem in Image Analysis. In the standard Bayesian approach the unknown original image is assumed to be a realization of a Markov random field on a finite two dimensional finite…