Generalized bit-planes for embedded codes

In many modern image compression techniques, the coefficients of an image transform are encoded by successive refinements. This is in general equivalent to successively encoding each bit-plane of the image transforms. Such methods, especially when the wavelet transform is employed, are among the state-of-the-art in image coding. In fact, several proposals to the JPEG 2000 standard use some sort of bit-plane encoding. Bit-plane encoding has been traditionally used as a scalar quantization technique, that is, each coefficient in individually decomposed in bit-planes. We analyze extensions of the bit-plane encoding concept to vectors, whereby each vector of the coefficients is decomposed in “vector bit-planes”. First, we formally describe the vector bit-plane representations, and then state a theorem concerning conditions for their existence. Next, we propose a modification to the proposed vector bit-plane representations and state a second theorem, which shows that the proposed modifications lead to much more robust algorithms. Simulation results are presented for the embedded encoding of wavelet coefficients of images, which confirm, the potential advantages of vector over scalar bit-plane representations. These strongly indicate that vector bit-plane representations should be further investigated