Hello, and welcome to the Paper of the Day (Po'D): Signal Processing Edition. Today's paper comes from our colleagues Mads Christensen, Jan Østergaard, and Søren Holdt Jensen:

In this paper, the authors look at the contribution of compressed sensing to finding sparse approximations of audio and speech signals using redundant dictionaries.

*On Compressed Sensing and Its Application to Speech and Audio Signals*, in Proc. Asilomar Conf. Signals, Systems, and Computers, 2009.In this paper, the authors look at the contribution of compressed sensing to finding sparse approximations of audio and speech signals using redundant dictionaries.

**The main reason this work is exciting is because it demonstrates how we can significantly reduce the dimensionality of the problem of finding sparse and efficient representations for high-dimensional data, such as sampled audio.**This means that I can keep working with large and redundant dictionaries, use an optimization method to build a representation based on minimizing the \ell_1-norm of the solution, and still be home in time for dinner. I do not need to rely only on greedy short-sighted methods of sparse approximation. The magic here is in how one can use compressed sensing to reduce the number of constraints involved in solving the problem -- but only as long as the signal being decomposed is sparse in the given dictionary. And there is the rub: since the sparsity of the signal is unknown a priori, we must guess it to ensure our measurement matrix will permit recovery of the solution. However, it appears that in the world of sparse*approximation*, even if we misjudge the sparsity, the solution will not be significantly worse than otherwise. That is good news!