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Image reconstruction based on an edge-sparsity assumption has become popular in recent years. Many methods of this type are capable of reconstructing nearly perfect edge-sparse images using limited data. In this paper, we present a method…
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.…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
Data augmentations have been widely studied to improve the accuracy and robustness of classifiers. However, the potential of image augmentation in improving GAN models for image synthesis has not been thoroughly investigated in previous…
Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in…
Solving non-convex regularized inverse problems is challenging due to their complex optimization landscapes and multiple local minima. However, these models remain widely studied as they often yield high-quality, task-oriented solutions,…
Self-supervised learning is crucial for super-resolution because ground-truth images are usually unavailable for real-world settings. Existing methods derive self-supervision from low-resolution images by creating pseudo-pairs or by…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
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…
Optical diffraction tomography measures the three-dimensional refractive index map of a specimen and visualizes biochemical phenomena at the nanoscale in a non-destructive manner. One major drawback of optical diffraction tomography is poor…
This paper considers the problem of signal denoising using a sparse tight-frame analysis prior. The L1 norm has been extensively used as a regularizer to promote sparsity; however, it tends to under-estimate non-zero values of the…
This work investigates the geometry of a nonconvex reformulation of minimizing a general convex loss function $f(X)$ regularized by the matrix nuclear norm $\|X\|_*$. Nuclear-norm regularized matrix inverse problems are at the heart of many…
Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction…
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…
This paper presents a practical method for finding the globally optimal solution to the sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to…
Image quality is the basis of image communication and understanding tasks. Due to the blur and noise effects caused by imaging, transmission and other processes, the image quality is degraded. Blind image restoration is widely used to…
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…
Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…