Many important sources of data including sub-band image and speech coefficients are highly peaked and can be well-modeled by the family of generalized Gaussian (GG) PDFs parameterized by a shape parameter /spl nu/. We present here algorithms for defining and quantizing to a Z lattice in which the boundary is optimized to the characteristics of GG sources, and show that these techniques lead to high performance and low complexity for bit rates and dimensions that are of interest in a number of practical coding applications. We derive an analytical description of the granular and overload distortion valid for low and moderate bit rates, and also provide a description of quantizer performance in the limit of high rate and dimension.

The ITU-T low-bit-rate video coding standard H.263 supports efficient transmission of digital video over narrow-band telecommunication channels. The standard provides an excellent framework for low bit rate video coding, and leaves substantial design flexibility for tasks such as motion estimation to the implementer. We propose an alternative to the sum of absolute difference (SAD) metric that is used as the criterion for identifying motion vectors in many video coding implementations. The SAD usually fails to identify the rate-distortion optimal motion vector for a block because it does not take into account of the number of bits used to code the motion vector. One solution which has been proposed in the past is to use the Lagrangian cost J=D+/spl lambda/R as the cost function in motion estimation. This allows near optimal motion vector search in the rate-distortion sense but is too complex to be used in a practical video coding system. We present an alternative motion estimation algorithm that considers rate-distortion trade-offs in a low complexity framework, resulting in both a higher coding efficiency and a faster encoding speed.

We describe a new wavelet image coding approach in which a 4-ary symbol set with two contexts is used to represent significant coefficient values and the lengths of zero runs between coefficients. This algorithm works by raster scanning within subbands, and therefore involves much lower addressing complexity than other algorithms such as zerotree coding that require the creation and maintenance of intersubband dependencies across different decomposition levels. Despite its simplicity, and the fact that these dependencies are not explicitly utilized, the algorithm presented here is competitive with the refinements of zerotree coding. Stack-run coding can also be applied in the absence of entropy coding, resulting in an even lower complexity coder which in many cases performs within 1 dB PSNR of the entropy coded version.

We describe a new image coding approach in which a 4-ary arithmetic coder is used to represent significant coefficient values and the lengths of zero runs between coefficients. This algorithm works by raster scanning within subbands, and therefore involves much lower addressing complexity than other algorithms such as zerotree coding that require the creation and maintenance of lists of dependencies across different decomposition levels. Despite its simplicity, and the fact that these dependencies are not explicitly utilized, the algorithm presented here is competitive with the best enhancements of zerotree coding. In addition, it performs comparably with adaptive subband splitting approaches that involve much higher implementation complexity.

Lattice vector quantization schemes offer high coding efficiency without the burden associated with generating and searching a codebook. The distortion associated with a given lattice is often expressed in terms of the G number, which is a measure of the mean square error per dimension generated by quantization of a uniform source. Subband image coefficients, however, are best modeled by a generalized Gaussian, leading to distortion characteristics that are quite different from those encountered for uniform, Laplacian, or Gaussian sources. We present here the distortion associated with Z, E/sub 8/, and Leech lattice quantization for coding of generalized Gaussian sources, and show that for low bit rates the Z lattice offers both the best performance and the lowest implementational complexity.

A fixed-rate lattice vector quantizer for generalized Gaussian (GG) sources is presented. By using the contour of constant probability of a generalized Gaussian source to bound the integer lattice, this vector quantizer in the limit of high dimension achieves optimal boundary gains for GG sources. Low-complexity techniques for rate control, optimal codevector search and enumeration are developed. This coder achieves 8.60 dB for a generalized Gaussian source with shape parameter of 0.5 at 1 bit/sample (compared with a rate distortion bound of 9.23 dB) and 32.62 dB for the 512/spl times/512 "Lena" image at 0.25 bpp without the use of entropy coding. By using two small lookup tables, the nearest codeword search operation can be performed multiply-free and the overall quantization process costs one multiply and a few adds per sample.