The M-term pursuit for image representation and progressive compression

This paper introduces a sparse signal representation algorithm in redundant dictionaries, called the M-term pursuit (MTP), with an application to image representation and scalable coding. The MTP algorithm belongs to the framework of the matching pursuit (MP) (S. Mallat and Z. Zhang, 1993); it expands the image into a linear combination of atoms, selected from a large collection of spatial atoms. The MTP relies on the concept of dictionary partitioning, i.e., as splitting the dictionary into L disjoint sub-dictionaries, each carrying some specific information. Then, it iteratively finds a K-term approximation, by selecting M atoms at a time, where M ≤ L, followed by an orthogonal projection. The approximation performances of the MTP algorithm have been shown to yield comparable results with those of the matching pursuit. However, it presents the advantage of a reduced computational complexity. For progressive image compression, an embedded quantization and coding step is applied on the series of obtained atoms based on the subset approach (A. Rahomoune, et al, 2004); to generate a flexible bitstream. The performances of the MTP image coder are finally shown to compare favorably against those of the state-of-the-art JPEG-2000 scheme, in terms of rate-distortion characteristics.