Reversible integer wavelet transforms allow both lossless and lossy decoding using a single bitstream. We present a new fully scalable image coder and investigate the lossless and lossy performance of these transforms in the proposed coder. The lossless compression performance of the presented method is comparable to JPEG-LS. The lossy performance is quite competitive with other efficient lossy compression methods.

In this work, we present coding techniques that enable progressive transmission when trellis coded quantization (TCQ) is applied to wavelet coefficients. A method for approximately inverting TCQ in the absence of least significant bits is developed. Results are presented using different rate allocation strategies and different entropy coders. The proposed wavelet-TCQ coder yields excellent coding efficiency while supporting progressive modes analogous to those available in JPEG.

As image coders evolve from DCT-based to wavelet-based designs, the latter must be enhanced to include capabilities currently supported by standards such as JPEG. Said and Pearlman (see IEEE Transactions on Circuits and Systems for Video Tech., vol.6, p.243-50, 1996) and Schwartz, Zandi and Boliek (see Proc. of SPIE, vol.2564, July 1995) have described approaches for incorporating progressive transmission capabilities within wavelet-based coders. All of these coders apply scalar quantization to wavelet transform coefficients and then apply sophisticated entropy coding methods to the quantized coefficients. In this paper, we present coding techniques that enable progressive transmission when trellis coded quantization (TCQ) is applied to the wavelet coefficients. While the trellis coded quantizer is more complex than the uniform scalar quantizer, comparable PSNR performance is achieved with a simple entropy coder. In addition, our use of sophisticated quantization and bit rate allocation algorithms enables the development of coders that are tuned for improved perceptual image quality.

Multiresolution methods have played a prominent role in image processing since the early eighties. Concurrently, multigrid methods have gained wide acceptance in numerical methods. These two concepts are similar in certain aspects. In this paper, we discuss these similarities in the context of image deconvolution problems. A unified space decomposition formulation linking multiresolution and multigrid methods is presented. In addition, certain earlier deconvolution schemes based on background-detail methods, Grenander's method of sieves etc. are interpreted as variations based on this common formulation.>