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Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…

Overfitting is one of the critical problems in deep neural networks. Many regularization schemes try to prevent overfitting blindly. However, they decrease the convergence speed of training algorithms. Adaptive regularization schemes can…

Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…

Recovering a signal from its Fourier magnitude is referred to as phase retrieval, which occurs in different fields of engineering and applied physics. This paper gives a new characterization of the phase retrieval problem. Particularly…

We propose a multiscale approach to time series autoregression, in which linear regressors for the process in question include features of its own path that live on multiple timescales. We take these multiscale features to be the recent…

Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…

We introduce a reinforcement learning (RL) based adaptive optimization algorithm for aerodynamic shape optimization focused on dimensionality reduction. The form in which RL is applied here is that of a surrogate-based, actor-critic policy…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…

PhaseLift, proposed by E.J. Cand\`{e}s et al., is one convex relaxation approach for phase retrieval. The relaxation enlarges the solution set from rank one matrices to positive semidefinite matrices. In this paper, a relaxation is employed…

Retrieval-Augmented Generation (RAG) systems for Large Language Models (LLMs) hold promise in knowledge-intensive tasks but face limitations in complex multi-step reasoning. While recent methods have integrated RAG with chain-of-thought…

We study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources subject to a single-letter average distortion constraint and a perception constraint belonging to the family of $f$-divergences. In…

We introduce a fast iterative non-local shrinkage algorithm to recover MRI data from undersampled Fourier measurements. This approach is enabled by the reformulation of current non-local schemes as an alternating algorithm to minimize a…

Modern large-scale recommender systems employ multi-stage ranking funnel (Retrieval, Pre-ranking, Ranking) to balance engagement and computational constraints (latency, CPU). However, the initial retrieval stage, often relying on efficient…

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…

Binary segmentation, which is sequential in nature is thus far the most widely used method for identifying multiple change points in statistical models. Here we propose a top down methodology called arbitrary segmentation that proceeds in a…

This paper considers the problem of identifying multivariate autoregressive (AR) sparse plus low-rank graphical models. Based on the corresponding problem formulation recently presented, we use the alternating direction method of…

In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a…

In this work, we propose an alternating low-rank decomposition (ALRD) approach and novel subspace algorithms for direction-of-arrival (DOA) estimation. In the ALRD scheme, the decomposition matrix for rank reduction is composed of a set of…

Anomaly detection on time series data is increasingly common across various industrial domains that monitor metrics in order to prevent potential accidents and economic losses. However, a scarcity of labeled data and ambiguous definitions…

Retrieval-Augmented Generation (RAG) is a core approach for enhancing Large Language Models (LLMs), where the effectiveness of the retriever largely determines the overall response quality of RAG systems. Retrievers encompass a multitude of…