Various applications in signal processing and machine learning give rise to highly structured spectral optimization problems characterized by low-rank solutions. Two important examples that motivate this work are optimization problems from phase retrieval and from blind deconvolution, which are designed to yield rank-1 solutions. An algorithm is described based on solving a certain constrained ...

We describe a data structure, called a priority range tree, which accommodates fast orthogonal range reporting queries on prioritized points. Let S be a set of n points in the plane, where each point p in S is assigned a weight w(p) that is polynomial in n, and define the rank of p to be r(p) = blogw(p)c. Then the priority range tree can be used to report all points in a threeor four-sided quer...

In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.

The drops are used to control the descents,  stabilize the bed level, and control the upstream water level in sloping channels with less slope than the ground slope. The current study presents a numerical analysis of hydraulic characteristics in the vertical drop using computational fluid dynamics. At first, the laboratory models were used for verification and choosing the best model of turbule...

It is challenging and inspiring for us to achieve high spatiotemporal resolutions in dynamic cardiac magnetic resonance imaging (MRI). In this paper, we introduce two novel models and algorithms to reconstruct dynamic cardiac MRI data from under-sampled k - t space data. In contrast to classical low-rank and sparse model, we use rank-one and transformed sparse model to exploit the correlations ...

We propose a new approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on constrained sensing vectors and a two-stage reconstruction method that consists of two standard convex optimization programs that are solved sequentially. Various methods for compre...

Assume we are given a sum of linear measurements of s different rank-r matrices of the form y = ∑s k=1Ak(Xk). When and under which conditions is it possible to extract (demix) the individual matrices Xk from the single measurement vector y? And can we do the demixing numerically efficiently? We present two computationally efficient algorithms based on hard thresholding to solve this low rank de...

We study the problem of reconstructing low-rank matrices from their noisy observations. We formulate the problem in the Bayesian framework, which allows us to exploit structural properties of matrices in addition to low-rankedness, such as sparsity. We propose an efficient approximate message passing algorithm, derived from the belief propagation algorithm, to perform the Bayesian inference for...

For any finitely generated module M with non-zero rank over a commutative one-dimensional Noetherian local domain, we study numerical invariant h(M) based on partial trace ideal of M. We its properties and explore relations between this the colength conductor. Finally apply to universally finite differentials ΩR/k, where R is complete k-algebra k perfect field, long-standing conjecture due R. W...