Now showing items 31-40 of 67
A Simple Proof for Recoverability of L1-Minimization: Go Over or Under?
It is well-known by now that L1 minimization can help recover sparse solutions to under-determined linear equations or sparsely corrupted solutions to over-determined equations, and the two problems are equivalent under ...
A Fast TVL1-L2 Minimization Algorithm for Signal Reconstruction from Partial Fourier Data
Recent compressive sensing results show that it is possible to accurately reconstruct certain compressible signals from relatively few linear measurements via solving nonsmooth convex optimization problems. In this paper, ...
User's Guide For YALL1: Your Algorithms for L1 Optimization
This User's Guide describes the functionality and basic usage of the Matlab package YALL1 for L1 minimization. The one-for-six algorithm used in the YALL1 solver is briefly introduced in the appendix.
The Behavior of Newton-Type Methods on Two Equivalent Systems from Linear Programming
Newton-type methods are fundamental techniques for solving optimization problems. However, it is often not fully appreciated that these methods can produce significantly different behavior when applied to two equivalent ...
An Interior-Point Algorithm for the Maximum-Volume Ellipsoid Problem
In this report, we consider the problem on finding the maximum-volume ellipsoid inscribing a given full-dimensional polytope in R^n defined by a finite set of affine inequalities. We present several formulations for the ...
The Effect of the Separation of Variables on the Molecular Replacement Method
Traditional approaches for solving the molecular replacement problem separate a six-dimensional optimization problem into two three-dimensional ones in order to reduce the computational cost. There are, however, serious ...
When is Missing Data Recoverable?
Suppose a non-random portion of a data vector is missing. With some minimal prior knowledge about the data vector, can we recover the missing portion from the available one? In this paper, we consider a linear programming ...
On Theory of Compressive Sensing via L_1-Minimization: Simple Derivations and Extensions
Compressive (or compressed) sensing (CS) is an emerging methodology in computational signal processing that has recently attracted intensive research activities. At present, the basic CS theory includes recoverability and ...
A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration
We generalize the alternating minimization algorithm recently proposed in  to effciently solve a general, edge-preserving, variational model for recovering multichannel images degraded by within- and cross-channel ...
Solving Semidefinite Programs via Nonlinear Programming, Part I: Transformations and Derivatives
In this paper, we introduce transformations that convert a large class of linear and/or nonlinear semidefinite programming (SDP) problems into nonlinear optimization problems over "orthants" of the form (R^n)++ × R^N, ...