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Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…
Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank…
We present a convex relaxation-based algorithm for large-scale general phase retrieval problems. General phase retrieval problems include i.a. the estimation of the phase of the optical field in the pupil plane based on intensity…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
Commercial retrospective video analytics platforms have increasingly adopted general interfaces to support the custom queries and convolutional neural networks (CNNs) that different applications require. However, existing optimizations were…
Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…
The mathematical theory of super-resolution developed recently by Cand\`{e}s and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of…
We present efficient implementations of atom reconfiguration algorithms for both CPUs and GPUs, along with a batching routine to merge displacement operations for parallel execution. Leveraging graph-theoretic methods, our approach derives…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
Image segmentation has come a long way since the early days of computer vision, and still remains a challenging task. Modern variations of the classical (purely bottom-up) approach, involve, e.g., some form of user assistance (interactive…
Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the…
This paper develops a unified high-order accumulative regularization (AR) framework for convex and uniformly convex gradient norm minimization. Existing high-order methods often exhibit a gap: the function-value residual decreases fast,…
We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step…
Regularization-based image restoration has remained an active research topic in computer vision and image processing. It often leverages a guidance signal captured in different fields as an additional cue. In this work, we present a general…