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Non-rigid 3D registration, which deforms a source 3D shape in a non-rigid way to align with a target 3D shape, is a classical problem in computer vision. Such problems can be challenging because of imperfect data (noise, outliers and…

Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…

This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…

This paper concerns a class of composite image reconstruction models for impluse noise removal, which is rather general and covers existing convex and nonconvex models proposed for reconstructing images with impluse noise. For this…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the…

As Computed Tomography (CT) scans are an essential medical test, many techniques have been proposed to reconstruct high-quality images using a smaller amount of radiation. One approach is to employ algebraic factorization methods to…

Time-of-flight neutron imaging offers complementary attenuation contrast to X-ray computed tomography (CT), coupled with the ability to extract additional information from the variation in attenuation as a function of neutron energy (time…

This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…

We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…

With recent advances in dynamic scanning probe microscopy techniques, it is now a routine to image the sub-molecular structure of molecules with atomically-engineered tips which are prepared via controlled modification of the tip…

In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…

A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…

Restricted isometry property (RIP), essentially stating that the linear measurements are approximately norm-preserving, plays a crucial role in studying low-rank matrix recovery problem. However, RIP fails in the robust setting, when a…

Over the past decade, reflection matrix microscopy (RMM) and advanced image reconstruction algorithms have emerged to address the fundamental imaging depth limitations of optical microscopy in thick biological tissues and complex media. In…

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

This paper is concerned with the fundamental problem of estimating chirp parameters from a mixture of linear chirp signals. Unlike most previous methods, which solve the problem by discretizing the parameter space and then estimating the…

The aim of this paper is to discuss some advanced aspects of image reconstruction in single-pixel cameras, focusing in particular on detectors in the THz regime. We discuss the reconstruction problem from a computational imaging perspective…

With the advent of infrared long-baseline interferometers with more than two telescopes, both the size and the completeness of interferometric data sets have significantly increased, allowing images based on models with no a priori…