Compressibility Constrained Sparse Representation With Learnt Dictionary for Low Bit-Rate Image Compression

Abstract

This paper proposes a compressibility constrained sparse representation (CCSR) approach to low bit-rate image compression using a learnt over-complete dictionary of texture patches. Conventional sparse representation approaches for image compression are based on matching pursuit (MP) algorithms. Actually, the weakness of these approaches is that they are not stable in terms of sparsity of the estimated coefficients, thereby resulting in the inferior performance in low bit-rate image compression. In comparison with MP, convex relaxation approaches are more stable for sparse representation. However, it is intractable to directly apply convex relaxation approaches to image compression, as their coefficients are not always compressible. To utilize convex relaxation in image compression, we first propose in this paper a CCSR formulation, imposing the compressibility constraint on the coefficients of sparse representation for each image patch. In addition, we work out the CCSR formulation to obtain sparse and compressible coefficients, through recursively solving the \(\ell _{1}\) -norm optimization problem of sparse representation. Given these coefficients, each image patch can be represented by the linear combination of texture elements encoded in an over-complete dictionary, learnt from other training images. Finally, low bit-rate image compression can be achieved, owing to the sparsity and compressibility of coefficients by our CCSR approach. The experimental results demonstrate the effectiveness and superiority of the CCSR approach on compressing the natural and remote sensing images at low bit-rates.