Basis selection in the presence of noise

We consider procedures to enhance the reliability of basis selection procedures with particular attention being given to methods based on minimizing diversity measures. To deal with noise in the data, basis selection procedures based on a Bayesian framework are considered. An algorithm based on the MAP estimation procedure is developed which leads to a regularized version of the FOCUSS algorithm. Another approach considered is to select basis vectors over multiple measurement vectors thereby achieving an averaging effect and enhancing the reliability. New diversity measures are presented for this purpose, and algorithms are derived for minimizing them.