  The investigation of the effects of sparsity or sparsity constraints in
signal processing problems has received considerable attention recently.
Sparsity constraints refer to the a priori information that the object or
signal of interest can be represented by using only few elements of a
predefined dictionary. Within this thesis, sparsity refers to the fact that a
vector to be estimated has only few nonzero entries. One specific field
concerned with sparsity constraints has become popular under the name
Compressed Sensing (CS). Within CS, the sparsity is exploited in order to
perform (nearly) lossless compression. Moreover, this compression is carried
out jointly or simultaneously with the process of sensing a physical quantity.
In contrast to CS, one can alternatively use sparsity to enhance signal
processing methods. Obviously, sparsity constraints can only improve the
obtainable estimation performance since the constraints can be interpreted as
an additional prior information about the unknown parameter vector which is to
be estimated. Our main focus will be on this aspect of sparsity, i.e., we
analyze how much we can gain in estimation performance due to the sparsity
constraints.
