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Many image processing applications benefited remarkably from the theory of sparsity. One model of sparsity is the cosparse analysis one. It was shown that using l_1-minimization one might stably recover a cosparse signal from a small set of…

Optical molecular tomographic imaging is to reconstruct the concentration distribution of photon-molecular probes in a small animal from measured photon fluence rates. The localization and quantification of molecular probes is related to…

Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…

We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…

We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to solve a large…

In the past decades, Computed Tomography (CT) has established itself as one of the most important imaging techniques in medicine. Today, the applicability of CT is only limited by the deposited radiation dose, reduction of which manifests…

Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…

We devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite structure. More specifically, we introduce a new class of estimating functions, which are obtained by…

In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…

Various types of parameter restart schemes have been proposed for accelerated gradient algorithms to facilitate their practical convergence in convex optimization. However, the convergence properties of accelerated gradient algorithms under…

Generalization problems in languages with binders involve computing the most common structure between expressions while respecting bound variable renaming and freshness constraints. These problems often lack a least general solution.…

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

This paper investigates a novel gradient algorithm, AGEM, using both energy and momentum, for addressing general non-convex optimization problems. The solution properties of the AGEM algorithm, including aspects such as uniformly…

In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…

Optimization lies at the core of modern deep learning, yet existing methods often face a fundamental trade-off between adapting to problem geometry and leveraging curvature utilization. Steepest descent algorithms adapt to different…

This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…

Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…

In this paper, we present a new algorithm, called MagnitudeCut, for recovering a signal from the phase of its Fourier transform. We casted our recovering problem into a new convex optimization problem, and then solved it by the block…