Invited Session Mon.1.H 1058

Monday, 10:30 - 12:00 h, Room: H 1058

Cluster 10: Implementations & software [...]

Testing environments for machine learning and compressed sensing


Chair: Katya Scheinberg



Monday, 10:30 - 10:55 h, Room: H 1058, Talk 1

Michael Friedlander
Spot: A linear-operator toolbox for Matlab

Coauthor: Ewout van den Berg


Linear operators are at the core of many of the most basic algorithms
for signal and image processing. Matlab's high-level, matrix-based
language allows us to express naturally many of the underlying matrix
operations - e.g., computation of matrix-vector products and
manipulation of matrices - and is thus a powerful platform on which to
develop concrete implementations of these algorithms. Many of the most
useful operators, however, do not lend themselves to the explicit
matrix representations that Matlab provides. This talk describes the
new Spot Toolbox, which aims to bring the expressiveness of Matlab's
built-in matrix notation to problems for which explicit matrices are
not practical. I will demonstrate features of the toolbox with
examples from compressed sensing and image reconstruction.



Monday, 11:00 - 11:25 h, Room: H 1058, Talk 2

Katya Scheinberg
Studying effects of various step selection strategies in first order approaches to compressed sensing and other composite optimization problems


We will discuss theoretical and practical implications of various strategies for choosing the prox parameter in prox gradient methods and related alternating direction methods. We will show extension of existing convergence rates for both accelerated and classical first-order methods. Practical comparison based on a testing environment for L1 optimization will be presented.



Monday, 11:30 - 11:55 h, Room: H 1058, Talk 3

Dirk Lorenz
Constructing test instances for basis pursuit denoising

Coauthor: Christian Kruschel


The number of available algorithms for the so-called Basis Pursuit Denoising problem (or the related LASSO-problem) is large and keeps growing. Similarly, the number of experiments to evaluate and compare these algorithms on different instances is growing.

In this talk, we discuss a methods to produce instances with exact solutions which is based on a simple observation which is related to the so called source condition from sparse regularization and the so-called dual certificate. We construct such dual-certificate by alternating projections onto convex sets and also by linear programming method. The method have been implemented in a MATLAB package L1TestPack.


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