An embedded wavelet image coder with parallel encoding and sequential decoding of bit-planes

Abstract

Wavelet-based coders are widely used in image compression. Many popular embedded wavelet coders are based on a data structure known as zerotree. However, there exists another category of embedded wavelet coders that are fast and efficient without employing zerotree. These coders are based on three key concepts: (1) wavelet coefficient reordering, (2) bit-plane partitioning, and (3) encoding of bit-planes with certain efficient variants of run-length coding. In this paper, we propose a novel method to construct a bit-plane encoder that can be used in this category of non-zerotree coders. Instead of encoding the bit-planes progressively, the bit-plane encoding process can be finished in one pass when multiple bit-plane encoders are activated concurrently. With this proposed method, traditional partitioned-block based parallel processing strategy is enhanced with another dimension (depth of bit-planes) of processing flexibility. This bit-plane encoder inherently targets parallel processing architecture. The final output bitstream can be compatible with that of the original sequential coder if compatibility is preferred over speed and memory efficiency.

Introduction

Wavelet transform-based image coding schemes have already found their wide usage in the scientific and industrial community. In many application scenarios such as image database indexing and retrieval, parallel processing capability is desirable because of the huge volume of data and real-time processing demand.

Although parallel wavelet image compression is an interesting research topic, so far a significant amount of work has only been done on parallel wavelet transform algorithms, which function as the first stage of a complete image coder. When it comes to parallel processing of the quantization and entropy coding stages, less work has been reported in the literature, which in the authors’ opinion results from the difficulty in parallelizing the zerotree-based coding methods since many wavelet image coding methods proposed up-to-date are based on the zerotree data structure.

The first zerotree-based embedded coding method proposed was EZW [1], in which clusters of insignificant (small magnitude) coefficients are encoded through single symbols. These clusters of coefficients are called zerotrees because of the quadtree-like arrangement of coefficients which exploits the residual cross-scale statistical dependency in a wavelet pyramid. Later, an enhanced zerotree-based technique was proposed as SPIHT [2], which uses a different pattern of parent–children relationship and achieves good compression performance even without an explicit entropy encoding stage.

Parallelization of the EZW algorithm was first reported in [3], where two approaches were proposed: (1) a straightforward parallelization which ensures that each processing element (PE) contains only entire zerotrees of wavelet coefficients, and (2) one PE is reserved for the collection of the symbols that have to be encoded. This PE reorders the symbols and encodes them. This approach results in higher complexity. In fact, the first approach can be generalized as local processing principle under which an image (a decomposed wavelet pyramid) can be partitioned into pixel (coefficient) blocks and each block can be compressed locally by a PE. This one-block-per-PE approach is also suggested in [4] for consideration of parallel execution in the JPEG2000 image coding system.

The parallelization of the SPIHT algorithm is more difficult because of the list structures it uses. The lists in the SPIHT cause variable and data-dependent memory requirement. The task of memory management on adding, dropping, and removing list nodes is complicated and undesirable in memory-constraint environments. To make it worse, managing a distributed list across multiple PEs is even more difficult. Some techniques have recently been proposed to remove the list structures from zerotree-based coders to make them more suitable for hardware implementation and parallel processing [5], [6], [7].

Because of the popularity of zerotree-based techniques, virtually no effort has been dedicated to parallelization of other equally efficient techniques, which may potentially be parallelized more easily and efficiently. One category of such algorithms is based on bit-plane coding [8] and run-length coding of binary sequence [9], [10], [11], [13]. The common features of these methods are: (1) the wavelet pyramid is mapped into a one-dimensional array and thereafter the coefficients within it are linearly indexed, (2) the wavelet pyramid is treated as multiple bit-planes and bit-planes are encoded following the order of decreasing significance, and (3) two-dimensional bit-planes are converted to one-dimensional binary sequences by linear reordering before the binary sequences are encoded by efficient run-length coders.

This paper demonstrates that the category of embedded coding methods mentioned above can easily and efficiently be mapped onto a multiple instruction multiple data (MIMD) architecture in the form of parallel bit-plane encoding. In other words, in addition to being segmented into blocks, wavelet pyramids can be sliced in another dimension (depth of bit-planes) into bit-planes as shown in Fig. 1. Furthermore, a bit-plane can be encoded by a PE without any communication with other PEs as proposed in this paper.

In the next section, we will describe our proposed parallel encoding and sequential decoding (PESD) method of parallelization. We use a modified wavelet difference reduction (MWDR) algorithm [12], which does not employ arithmetic coding, as our example although the method we propose can readily be applied to other data-independent schemes such as progressive wavelet coding (PWC) [11]. The method proposed in Section 2 is extended to cover bitstream compatibility in Section 3. The decoding procedure is discussed in Section 4. Experimental results are presented in Section 5. The paper ends with concluding remarks in Section 6.