Fast Wavelet Packet Image Compression

Current standard algorithms for storage and transmission of digitized images start with a compression method and ends with a decompression method for recovery of a good replica of the original picture. Unfortunately any recipe leading to significant compression rates involves some loss of information, and as such has to be matched to the nature of the image, and to our tolerance of error. The main defect of the block DCT methods (such as JPEG) is due to the limitation put on the size of the blocks and the inability to adapt the patterns to the nature of the picture. Another defect becomes apparent when reaching high compression rates: – the blocks used for compression start to be visible in the reconstructed picture. An answer to this problem can be provided by using wavelets to expand the image, instead of 8x8 DCT blocks. Wavelets yield a multiscale decomposition: low frequency trends occurring at a large scale in the image, can be as efficiently coded as local singularities, such as edges. Wavelets with many vanishing moments yield sparse decompositions of piece-wise smooth surfaces ; therefore they provide a very appropriate tool to compactly code smooth images [1, 9]. Wavelets, however, are ill suited to represent oscillatory patterns. To alleviate this issue much larger libraries of waveforms, called wavelet packets [4], have been developed. In the two dimensional case wavelet packets are patterns that can vary in scale, oscillation, and location. In order to select an orthonormal basis among all the wavelet packets, these patterns are matched to the image, and a selection of best matches which are sufficient for an efficient reconstruction is made. The selected collection of patterns is called the “best basis” [5]. When coding images that contain amixture of smooth and textured features, the best basis algorithm is always trying to find a compromise between two conflicting goals: – describe the large scale smooth regions, and describe the local textures. In [8], the optimal basis is chosen according to the rate-distortion criterion. Very recently some authors have proposed to use wavelet packets to characterize texture and code images [3, 6]. The main contribution of this paper is a new fast wavelet packet compression algorithm which encodes very efficiently textured images. This fast wavelet packet compression technique relies on four stages: