Binary decompositions for high-order entropy coding of grayscale images

High-order entropy coding (HOEC) has the potential to provide higher compression ratios than the usually used zero-order entropy coding (ZOEC) approaches. However, serious implementation difficulties severely limit the practical value of HOEC for grayscale image compression. We examine the bit-plane decomposition (BPD) representation as a simple alternative that bypasses some of the implementation difficulties of HOEC. We show, however, that BPD introduces undesired coding overhead when used to represent grayscale images. We therefore propose a new binary image representation called magnitude-based binary decomposition (MBBD) which avoids any coding overhead when used to represent grayscale images. Thus, MBBD both bypasses the implementation difficulties of HOEC and does not have the drawbacks of the BPD. We present numerical experiments that verify the theoretical analysis of the BPD and MBBD representations. In addition, our experiments demonstrate that MBBD-HOEC yields better results than ZOEC for lossy image compression and is also very effective for progressive image transmission.