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This paper addresses the question of what exactly is an analogue of the preconditioned steepest descent (PSD) algorithm in the case of a symmetric indefinite system with an SPD preconditioner. We show that a basic PSD-like scheme for an…

Convolutional neural networks (CNNs) have recently achieved remarkable performance in positron emission tomography (PET) image reconstruction. In particular, CNN-based direct PET image reconstruction, which directly generates the…

Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…

Deep learning-based reconstruction of positron emission tomography(PET) data has gained increasing attention in recent years. While these methods achieve fast reconstruction,concerns remain regarding quantitative accuracy and the presence…

We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible…

Image restoration algorithms such as super resolution (SR) are indispensable pre-processing modules for object detection in degraded images. However, most of these algorithms assume the degradation is fixed and known a priori. When the real…

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

Medical image reconstruction with pre-trained score-based generative models (SGMs) has advantages over other existing state-of-the-art deep-learned reconstruction methods, including improved resilience to different scanner setups and…

Dynamic positron emission tomography (dPET) image reconstruction is extremely challenging due to the limited counts received in individual frame. In this paper, we propose a spatial-temporal convolutional primal dual network (STPDnet) for…

Objective:This study introduces a residual error-shifting mechanism that drastically reduces sampling steps while preserving critical anatomical details, thus accelerating MRI reconstruction. Approach:We propose a novel diffusion-based SR…

Purpose: Neural network image reconstruction directly from measurement data is a relatively new field of research, that until now has been limited to producing small single-slice images (e.g., 1x128x128). This paper proposes a novel and…

This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…

Deep learning based PET image reconstruction methods have achieved promising results recently. However, most of these methods follow a supervised learning paradigm, which rely heavily on the availability of high-quality training labels. In…

Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…

Compressed Sensing (CS) significantly speeds up Magnetic Resonance Image (MRI) processing and achieves accurate MRI reconstruction from under-sampled k-space data. According to the current research, there are still several problems with…

Single-image super-resolution (SISR) typically focuses on restoring various degraded low-resolution (LR) images to a single high-resolution (HR) image. However, during SISR tasks, it is often challenging for models to simultaneously…

PET image reconstruction is challenging due to the ill-poseness of the inverse problem and limited number of detected photons. Recently deep neural networks have been widely and successfully used in computer vision tasks and attracted…

In this paper, we analyze different preconditionings designed to enhance robustness of pure-pixel search algorithms, which are used for blind hyperspectral unmixing and which are equivalent to near-separable nonnegative matrix factorization…

In biological research, fluorescence staining is a key technique to reveal the locations and morphology of subcellular structures. However, it is slow, expensive, and harmful to cells. In this paper, we model it as a deep learning task…

Deep learning has been widely used for solving image reconstruction tasks but its deployability has been held back due to the shortage of high-quality training data. Unsupervised learning methods, such as the deep image prior (DIP),…