相关论文: Epigraphical Relaxation for Minimizing Layered Mix…

In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…

Here we present new joint reconstruction and regularization techniques inspired by ideas in microlocal analysis and lambda tomography, for the simultaneous reconstruction of the attenuation coefficient and electron density from X-ray…

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…

Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified…

The rank minimization problem is to find the lowest-rank matrix in a given set. Nuclear norm minimization has been proposed as an convex relaxation of rank minimization. Recht, Fazel, and Parrilo have shown that nuclear norm minimization…

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…

In Transformer models, non-GEMM (non-General Matrix Multiplication) operations -- especially Softmax and Layer Normalization (LayerNorm) -- often dominate hardware cost due to their nonlinear nature. To address this, previous approximation…

This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…

Many geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given noisy measurements of a subset of their pairwise relative transforms. This problem is…

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…

Massive multiple-input multiple-output (MIMO) systems employing one-bit digital-to-analog converters offer a hardware-efficient solution for wireless communications. However, the one-bit constraint poses significant challenges for precoding…

Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the l1q norm with q>1 is attractive in many applications of…

This paper presents computationally feasible rank-one relaxation algorithms for the efficient simulation of a time-incremental damage model with nonconvex incremental stress potentials in multiple spatial dimensions. While the standard…

In compressed sensing one uses known structures of otherwise unknown signals to recover them from as few linear observations as possible. The structure comes in form of some compressibility including different notions of sparsity and low…

In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…

We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM,…

The present paper deals with the data-driven design of regularizers in the form of artificial neural networks, for solving certain inverse problems formulated as optimal control problems. These regularizers aim at improving accuracy,…