  This article introduces a new signal analysis method, which can be
interpreted as a principal component analysis in sparse decomposition of the
signal. The method, called principal basis analysis, is based on a novel
criterion: reproducibility of component which is an intrinsic characteristic of
regularity in natural signals. We show how to measure reproducibility. Then we
present the principal basis analysis method, which chooses, in a sparse
representation of the signal, the components optimizing the reproducibility
degree to build the so-called principal basis. With this principal basis, we
show that the underlying signal pattern could be effectively extracted from
corrupted data. As illustration, we apply the principal basis analysis to image
denoising corrupted by Gaussian and non-Gaussian noises, showing better
performances than some reference methods at suppressing strong noise and at
preserving signal details.
