Rank-adaptive signal processing (RASP) a subspace approach to biological signal analysis .I. Principles

In many biomedical signal processing problems, the signal of interest is corrupted by noise and interference from other sources. A method to recover the signal is to decompose the data space into orthogonal subspaces through singular-value decomposition (SVD). Because of the conservation of energy in the time and SVD domains, these subspaces correspond to the various signal and noise components contained in the data. To filter the noise, the data is projected onto the desired signal subspace by simply setting the noise singular values in the singular value spectrum of the data to zero. The purpose of this paper is to describe the theoretical basis for the subspace approach, an alternative method of signal estimation in the presence of additive noise and interference. We describe the principles of a rank adaptive signal processing (RASP) approach to biomedical signal processing.