The mergence of fast, embeddable parallel processors such as SIMD meshes and networked multiprocessors has motivated increased parallel algorithm development for image and signal processing (ISP) and automated target recognition (ATR). Among such applications are real-time video compression for Internet communication, videotelephony, and videoteleconferencing. In general, image or signal compression transforms tend to be attractive candidates for parallel implementations. For example, due to a rectangular, non-overlapping partition structure, block-oriented transforms such as JPEG can be processed in pipeline fashion. In contrast, implementational challenges accrue as a result of between-block data and control dependencies encountered in various pyramid-structured or hierarchical compression transforms such as wavelet-based coding. This paper summarizes ongoing research in the mapping of image compression transforms to SIMD-parallel computers. Three classes of algorithms are considered: (1) streaming, (2) block-oriented, and (3) hierarchically structured. It is shown that classes 1 and 2 are suitable for SIMD computation, particularly where mesh segments can be connected to form a pipeline. Computation is facilitated by modifying a SIMD mesh to form a brute-force synchronous MIMD processor, which is called a multi-SIMD or MSIMD architecture. Several designs for pipelined compression transform implementation on an MSIMD mesh are analyzed in terms of critical computational complexity and error. Analysis also emphasize theory, software, and parallelism required to support resolution of data and control dependencies encountered in ISP/ATR practice.