Abstract
This paper introduces a modified set partitioning in hierarchical trees (SPIHT) algorithm that reduces the number of comparison operations and, consequently, the execution time needed to encode an image as compared to the SPIHT algorithm. The threshold of each independent subband is calculated after applying the discrete wavelet transform to the image. Scanning of the sets inside the subbands is determined by the magnitude of the thresholds that establishes a hierarchical scanning not only for the set of coefficients with larger magnitude, but also for the subbands. The algorithm uses the set partitioning technique to sort the transform coefficients. Results show that the modified SPIHT significantly reduces the number of operations and the execution time without sacrificing visual quality and the PSNR of the recovered image.
Highlights
The performance of the proposed modified set partitioning in hierarchical trees (SPIHT) is examined and compared with SPIHT, Set partitioning in hierarchical frequency bands (SPHFB), LMSPIHT, and Fang et al.[22] methods using the images of Lena, Barbara, and Mandrill at 8 bpp monochrome 512 × 512 size.[32]
peak signal-to-noise ratio (PSNR), visual quality, performance with respect to the number of comparison operations in sorting passes, and time performance were compared with those obtained with SPIHT (Ref. 34) and with other algorithms
The comparison operations were counted during the sorting passes, and the execution time was taken including the initialization stage up to the end of the encoding process
Summary
It has been proven that image compression algorithms based on the discrete wavelet transform (DWT) provide high coding efficiency for natural images.[1,2,3,4,5,6] DWT has desirable properties, such as efficient multiresolution representation, scalability, vanishing moments, decorrelation, energy compaction, and embedded coding with progressive transmission, which are suitable for image compression.[7]. A modified SPIHT algorithm for image coding, which combines the SPIHT lists and hierarchical subband scanning to save comparison operations during sorting passes, is proposed. Two major modifications are proposed: (1) the calculation of one threshold per subband to impose a hierarchical scanning of sets with higher energy and, in contrast to the SPIHT, (2) the LIS must be initially empty and is populated with coordinates of sets in the subbands of higher hierarchy to avoid unnecessary entries to the list.
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