Application of total least squares (TLS) to the design of sparse signal representation dictionaries

Sparse signal representation has been the subject of much research in recent years in a variety of applications. We address the problem of learning a dictionary of waveforms from a given set of data signals, which may then be used to provide efficient and meaningful signal decompositions. We motivate and develop a total least squares (TLS) based algorithm. Through a series of simulations using a known test-case dictionary, it is shown that the TLS algorithm gives a substantial performance improvement over a previously proposed least squares (LS) algorithm in correctly learning the generating dictionary vectors.