Progressive Wavelet Coding of Images

Abstract Fast and efficient image compression can be achieved with the progressive wavelet coder (PWC)introduced in this paper. Unlike many previous wavelet coders, PWC does not rely on zerotreesor other ordering schemes based on parent-child wavelet relationships. PWC has a very simplestructure, based on two key concepts: (1) data-independent reordering and blocking, and (2) low-complexity independent encoding of each block via adaptive Rice coding of bit planes. In thatway, PWC allows for progressive image encoding that is scalable both in resolution and bit rate,with a fully embedded bitstream. PWC achieves a rate vs. distortion performance that is compa-rable to that of the state-of-the-art SPIHT (set partitioning in hierarchical trees) coder, but with abetter performance/complexity ratio. 1. Introduction In most applications, image (picture) data is usually transmitted in compressed form. For exam-ple, Web pages and digital cameras use compressed image formats, with JPEG (Joint Photo-graphic Experts Group [1]) being the most popular when the image does not need to be recon-structed exactly (lossy compression). In many cases, such as in broadcast transmission with re-ceivers connected via channels with different bandwidths, it is desirable that the transmission beprogressive. With progressive transmission, the transmitter can send a subset of the original bit-stream for a group of receivers; each subset can be chosen in order to achieve a desired level ofresolution and fidelity. In layered transmission systems, the bitstream is decomposed in a smallnumber of subsets (layers), in order of resolution and/or fidelity. Each receiver subscribes to asmany layers as its connection bandwidth will allow.A particularly useful form of progressive image coding is the one in which the bitstream isembedded, that is, representations of the image at any rate up to the encoding rate can be ob-tained simply by keeping the bitstream prefix corresponding to a desired rate. Embedded encod-ing can be achieved simply by applying the well-known bit-plane encoding technique [2] to thescalar-quantized wavelet coefficients. The most significant bit planes will naturally contain manyzeros, and therefore can be compressed without loss via entropy coders such as run-length cod-ers. Although such straightforward bit-plane encoding is not much effective when applied to theoriginal image samples [3], it can lead to reasonable performance (sometimes even better thanJPEG) when applied to quantized wavelet coefficients.Bit-plane encoding is more efficient if we reorder the wavelet coefficient data in such a waythat coefficients with small absolute values tend to get clustered together. That will translate intolonger runs of zeros in the bit planes, which can be encoded at lower bit rates. An efficient algo-rithm for achieving such clustering is the embedded zerotree wavelet (EZW) coder [4], which isbased in a straightforward concept. If a wavelet coefficient at a particular scale (resolution level)and spatial location – a parent coefficient – has magnitude below a certain threshold, then it islikely that coefficients at subsequent scales (higher resolution levels) and at the same spatial lo-cations – the offspring – also have magnitudes below that threshold. In that way, the bits in each