Principal Basis Analysis in Sparse Representation
This work addresses signal extraction and denoising for applications like image processing, but it appears incremental as it builds on sparse representation and principal component analysis concepts.
The authors tackled the problem of extracting underlying signal patterns from corrupted data by introducing principal basis analysis, a new signal analysis method based on reproducibility in sparse representations, and demonstrated its effectiveness in image denoising with better performance than reference methods in suppressing noise and preserving details.
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.