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Motivation

Compressed sensing has seen enormous growth in the last five years since its introduction in 2006. It has by now become a key concept in various areas of applied mathematics, computer science, and electrical engineering. The surprising key fact is that high-dimensional signals, which allow a sparse representation by a suitable basis or, more generally, a frame, can be recovered from what was previously considered highly incomplete linear measurements by using efficient algorithms. Applications may be found in a wide range of areas including signal and image processing as well as in the representation of solutions to ODEs and PDEs and other computational frameworks. When sparse solutions exist, several important questions need to be answered. For example: What are suitable frames? How can the sparse signals be determined? How can the methods be made efficient in the context of high-dimensional data? These questions inevitably lead to problems in optimization, frame theory and numerical linear algebra, such as efficient methods for 1 minimization, fast sparse solution methods for under-determined linear systems, and the combination of techniques from these different fields.

Goal of the Workshop

Therefore this workshop shall specifically focus on the intersections between the areas com- pressed sensing, frame theory, numerical linear algebra, and optimization theory, most of which emerged during the last few years. Its main goal is to initiate communications and collaborations between the leading experts of the different research areas. The workshop therefore will include, but is not limited to, the following research areas:

• Compressed sensing
• Dictionary learning, sparse dictionaries, sparse approximation
• Theory of redundant systems: Frame Theory
• Sparse recovery and approximation algorithms and their analysis
• Efficient l1-solvers
• Heuristics and exact algorithms for l0-solutions
• Applications: Solvers of differential equations and partial differential equations, data analysis and processing, inverse problems, etc.