Research On All Phase Biorthogonal Transform And Its Applications In Image Coding

Orthogonal transform has been widely applied to digital signal processing, from data compression to signal restoration. Meanwhile, reports on biorthogonal transform (BT) are greatly less than the ones on orthogonal transform. Recently, one new member in the family of BTs, named all phase biorthogonal transform (APBT), has become a highlight due to its reasonable performance in image coding. The objective of this paper is to make an improvement of APBT's coding performance and to enrich its applications in image coding.All phase (discrete cosine / inverse discrete cosine / Walsh) biorthogonal transforms are introduced after the explanation for design of all phase sequency filters. Another new BT presented in this paper which is called linear decaying discrete cosine biorthogonal transform, and three transforms above can be used as substitutes for discrete cosine transform (DCT) to implement the well-known JPEG scheme. The details of JPEG scheme based on BT (BT-JPEG) are selectively discussed. The coding results of BT-JPEG are compared with the JPEG scheme based on DCT (DCT-JPEG), which indicate that blocking artifacts in BT-JPEG are reduced at low bit rates.A deblocking algorithm using noise injection followed by image denoising (NIFID) is coupled with BT-JPEG to eliminate blocking artifacts at low bit rates. Results show that NIFID algorithm provides both objective and subjective improvements to the blocky image.Since progressive image coding has easy-controlled bit rates and high coding efficiency, two progressive image coding algorithms based on BT, named BT-EZW and BT-SPHIT, are designed, according to the principles of embedded zerotree wavelet (EZW) coding and set partitioning in hierarchical trees (SPIHT) algorithm, respectively. Both BT-EZW and BT-SPIHT produce compression results that significantly outperform DCT-JPEG at low bit rates.