Compressed Sensing: High Resolution Radar, Identification of Sparse Matrices

Sometimes I get to find preprints that are not yet on the Rice Resource page. Here are some:

Matthew Herman and Thomas Strohmer just came out with a preprint on High Resolution Radar via Compressed Sensing. The abstract reads:

A stylized compressed sensing radar is proposed in which the time-frequency plane is discretized into an N×N grid. Assuming the number of targets K is small (i.e., K  N2), then we can transmit a sufficiently “incoherent” pulse and employ the techniques of compressed sensing to reconstruct the target scene. A theoretical upper bound on the sparsity K is presented. Numerical simulations verify that even better performance can be achieved in practice. This novel compressed sensing approach offers great potential for better resolution over classical radar.

As for any new technique, when being compared with techniques that have been used for decades, it is hard to make a breakthrough. Here this difficulty seems to lie more in the sophistication of the target matching currently used than the detection per se. For the detection by this "stylised" approach, one seems to have an enormous gain in the resolution. The compressed sensing radar has a resolution of 1/(2 sqrt( N)) whereas a similar classical radar has a resolution of 1/2.


Identification of Matrices having a Sparse Representation by Jared Tanner, Gotz E. Pfander and Holger Rauhut. The abstract reads:

We consider the problem of recovering a matrix from its action on a known vector in the setting where the matrix can be represented efficiently in a known matrix dictionary. Connections with sparse signal recovery allows for the use of efficient reconstruction techniques such as Basis Pursuit (BP). Of particular interest is the dictionary of time–frequency shift matrices and its role for channel estimation and identification in communications engineering. We present recovery results for BP with the time–frequency shift dictionary and various dictionaries of random matrices.