Significant atom determination of basis pursuit decomposition

Atomic decomposition methods have been introduced as an alternative to classical signal representation. The use of redundant dictionaries in decomposition methods provides an adaptive signal processing technique. The choice of atoms to represent the signal of interest depends on the decomposition method chosen. In most cases, a highly sparse representation is desired. We examine basis pursuit (BP) decomposition of signals synthesised from elements not contained in the decomposition dictionary, real electroencephalogram (EEG) and whale signals in an effort to define significant atoms. Matching pursuit (MP) decomposition is then used as a reference for sparsity comparison with BP.