Sparsity and Compressed Sensing in Inverse Problems

This chapter is concerned with two important topics in the context of sparse recovery in inverse and ill-posed problems. In first part we elaborate condi-tions for exact recovery. In particular, we describe how both `1-minimization and matching pursuit methods can be used to regularize ill-posed problems and more-over, state conditions which guarantee exact recovery of the support in the sparse case. The focus of the second part is on the incomplete data scenario. We discuss ex-tensions of compressed sensing for specific infinite dimensional ill-posed measure-ment regimes. We are able to establish recovery error estimates when adequately relating the isometry constant of the sensing operator, the ill-posedness of the un-derlying model operator and the regularization parameter. Finally, we very briefly sketch how projected steepest descent iterations can be applied to retrieve the sparse solution

THE ANDRES PROJECT: ANALYSIS AND DESIGN OF RUN-TIME RECONFIGURABLE, HETEROGENEOUS SYSTEMS

Today’s heterogeneous embedded systems combine components from different domains, such as software, analogue hardware and digital hardware. The design and implementation of these systems is still a complex and error-prone task due to the different Models of Computations (MoCs), design languages and tools associated with each of the domains. Though making such systems adaptive is technologically feasible, most of the current design methodologies do not explicitely support adaptive architectures. This paper present the ANDRES project. The main objective of ANDRES is the development of a seamless design flow for adaptive heterogeneous embedded systems (AHES) based on the modelling language SystemC. Using domain-specific modelling extensions and libraries, ANDRES will provide means to efficiently use and exploit adaptivity in embedded system design. The design flow is completed by a methodology and tools for automatic hardware and software synthesis for adaptive architectures. 1