Locating zerotrees in a wavelet transform allows encoding of sets of coef cients with a single symbol. It is an ef cient means of coding if the overhead to identify the locations is small compared to the size of the zerotree sets on the average.It is advantageous in this regard to de ne classes of zerotrees according to the levels from the root until the remainder of the tree contains all zeroes. We call a tree with all zeroes except for the top k levels a degree-k zerotree. A degree-k zerotree coder is one that can encode degree-0 through degree-k zerotrees. We quantify the bit savings of a degree-k 2 over a degree-k 1 , k 2 > k 1 , coder. Because SPIHT is a degree-2 zerotree coder and EZW a degree-0 zerotree coder, we are able to explain the superior ef ciency of SPIHT. Finally, we gather statistics of degree-k zerotrees for different values of k in the bitplanes of several image wavelet transforms to support our analysis of the coding performance of degree-k zerotree coders.

An image coding algorithm, PROGRES (Progressive Resolution Coding), for a high speed resolution scalable decoding is proposed. The algorithm is designed based on a prediction of the decaying dynamic ranges of wavelet subbands.Most interestingly, because of the syntactic relationship between two coders, the proposed method costs very similar amount of bits as used by uncoded (i.e. not entropy coded) SPIHT. The algorithm bypasses bit-plane coding and complicated list processing of SPIHT in order to obtain a considerable speed improvement, giving up quality scalability, but without compromising coding ef ciency. Since each tree of coef cients is separately coded, where the root of the tree corresponds to the coef cient in LL subband, the algorithm is easily extensible to random access decoding.The algorithm is designed and implemented for both 2D and 3D wavelet subbands. Experiments show that the decoding speeds of proposed coding model are four times and nine times faster than uncoded 2D-SPIHT and 3D-SPIHT respectively, with almost the same decoded quality. The higher decoding speed gain in a larger image source validates the suitability of the proposed method to a very large scale image encoding and decoding.In the Appendix, we explain the syntactic relationship of the proposed PROGRES method to uncoded SPIHT, and demonstrate that in the lossless case the bits sent to the codestream for each algorithm are identical, except that they are sent in different order.

Daala is a new royalty-free video codec that attempts to compete with state-of-the-art royalty-bearing codecs. To do so, it must achieve good compression while avoiding all of their patented techniques. We use technology that is as different as possible from traditional approaches to achieve this. This paper describes the technology behind Daala and discusses where it fits in the newly created AV1 codec from the Alliance for Open Media. We show that Daala is approaching the performance level of more mature, state-of-the art video codecs and can contribute to improving AV1.

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For faster random access of a target image block, a bi-section idea is applied to link image blocks. Conventional methods configure the blocks in linearly linked way, for which the block seek time entirely depends on the location of the block on the compressed bitstream. The block linkage information is configured such that binary search is possible, giving the worst case block seek time of log 2 n , for n blocks. Experimental results with 3D-SPIHT on video sequences show that the presented idea gives substantial speed improvement with minimal bit overhead.