Related papers: Fixed-Point and Objective Convergence of Plug-and-…

Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…

Ptychography is a coherent diffraction imaging method that uses phase retrieval techniques to reconstruct complex-valued images. It achieves this by sequentially illuminating overlapping regions of a sample with a coherent beam and…

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…

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and…

Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable…

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…

It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, popular regularization methods have been the penalized Variational approaches. In recent years, the…

Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…

Matrix completion has attracted much interest in the past decade in machine learning and computer vision. For low-rank promotion in matrix completion, the nuclear norm penalty is convenient due to its convexity but has a bias problem.…

How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…

We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the $\ell_0$ norm. Specifically, the $\ell_0$ model has an objective function that is the sum of a convex fidelity term and a…

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based on multiscale…

Coherent lidar uses a chirped laser pulse for 3D imaging of distant targets. However, existing coherent lidar image reconstruction methods do not account for the system's aperture, resulting in sub-optimal resolution. Moreover, these…

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…

Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image denoisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications…

Plug and Play (PnP) methods achieve remarkable results in the framework of image restoration problems for Gaussian data. Nonetheless, the theory available for the Gaussian case cannot be extended to the Poisson case, due to the…

Diffusion models have found extensive use in solving inverse problems, by sampling from an approximate posterior distribution of data given the measurements. Recently, consistency models (CMs) have been proposed to directly predict the…

Selecting an appropriate prior to compensate for information loss due to the measurement operator is a fundamental challenge in imaging inverse problems. Implicit priors based on denoising neural networks have become central to widely-used…