Sparse Signal Processing
It is well known that under-determined linear systems of equations may admit infinitely many solutions. Within the field of sparse signal processing, we are interested in those solutions, where the unknown vector is sparse, i.e., most of its coefficients are zero. In mathematical terms, this coefficient structure can be expressed as a union of subspaces constraint on the unknowns. Because Newton's method fails to identify sparse solutions, new algorithms have been developed which are capable of finding these solutions efficiently. For instance, under-determined linear systems of equations arise quite naturally in nonlinear estimation problems when parameters are discretized onto a grid to reduce the computational complexity.
Sparse signal processing is used in the following fields of research at our institute: