Analysis and Application of Lattice Vector Quantization Using Mixture Models and Bit-Plane Coding
MetadataShow full item record
This thesis studies lattice vector quantization (LVQ) with application to audio and image sources. The performance of nonzero pulse amplitude quantization implicit in algebraic codebook code-excited linear prediction (ACELP) is examined and it is demonstrated that the quantization used in ACELP is effective in a rate-distortion sense at the encoding rates commonly used. A block-based Gaussian mixture model (GMM) is used to model the marginal distribution and the block energy distribution of transform audio data. The expectation-maximization algorithm is used to estimate the GMM parameters. A GMM-based rate-distortion function is derived and shown to closely match the observed spherical LVQ performance. Then, we move forward to the lattice VQ on transformed image. The GMM is used to motivate a subband image coding algorithm based on lattice-based spherical VQ and lattice-based pyramid VQ. The algorithm partitions a subband image into blocks of various sizes, depending on their energy and complexity constraints on the enumeration encoding of lattice codevectors. Using the cubic lattice, the algorithm provides performance competitive with the set partitioning in hierarchical trees (SPIHT) algorithm. A bit-plane coding method is developed for the encoding of binary lattice codevectors as binary codewords, yielding an embedded bitstream. In sign-magnitude representation, only a few least significant bit-planes are constrained due to the structure of the lattice, while there is no restriction on other more significant bit-planes. Simple encoding methods for the lattice-defining bit-planes of the $D_4$, $RE_8$, and Barnes-Wall 16-dimensional lattices are described. Simulation results for these lattices show that partial decoding of the resulting embedded bitstream provides about the same performance as for the integer lattice. When the entire bitstream is fully decoded, the granular gain of the lattice is realized.