Multilayered, blocked formal concept analyses for adaptive image compression

Abstract

Formal Concept Analysis (FCA) decomposes a matrix into a set of sparse matrices capturing its underlying structure. A similar task for real-valued data, transform coding, arises in image compression. Existing cosine transform coding for JPEG image compression uses a fixed, decorrelating transform; however, compression is limited as images rarely consist of pure cosines. The question remains whether an FCA adaptive transform can be applied to image compression. We propose a multi-layer FCA (MFCA) adaptive ordered transform and Sequentially Sifted Linear Programming (SSLP) encoding pair for adaptive image compression. Our hypothesis is that MFCA's sparse linear codes (closures) for natural scenes, are a complete family of ordered, localized, oriented, bandpass receptive fields, predicted by models of the primary visual cortex. Results on real data demonstrate that adaptive compression is feasible. These initial results may play a role in improving compression rates and extending the applicability of FCA to real-valued data. © 2014 Springer International Publishing.