A fixed-rate product pyramid vector quantization using a Bayesian model

Fast algorithm for pyramid vector quantization

“…The concept has been later applied to other different sources (as Gaussian, , generalized Gaussian, etc.) [2]. Generally, the PVQ can be successfully used for coding -dimensional vector sources where the distribution of entropy is restricted to the sphere (1) 1070-9908/01$10.00 © 2001 IEEE is near the entropy of the uniform distribution on the same sphere.…”

“…The most important part of PVQ schemes is an enumerative bijective mapping (3) which uniquely determines the codeword with length . It can be implemented by the recursive calculation of pyramid numbers [3], i.e., with 1 for all and 0 the is determined by (4) Let be defined as the number of pyramid points on all spheres with a radius not greater than , i.e., number of points in with (5) A can be calculated recursively [2], for fixed by (6) and for fixed by (7) with 1, 2 1, 1, 2 1, and 0 for each 0, 0. Finally, a fast coding and decoding PVQ algorithm for the points of a given pyramid encoding vector with an index can be calculated using the following algorithm.…”

“…Generally, the PVQ can be successfully used for coding -dimensional vector sources where the distribution of entropy is restricted to the sphere (1) 1070-9908/01$10.00 © 2001 IEEE is near the entropy of the uniform distribution on the same sphere. The -dimensional pyramid lattice with a radius of is defined as (2) that is, as a set of all the vectors from with integer components. Let be the pyramid number, i.e., number of the lattice points (determined by vectors constituting ) on the surface of the sphere with radius .…”

“…A promising solution for fast VQ is pyramid vector quantization (PVQ). Such a fast coding/decoding algorithm was developed by Filip and Ruf [2]. This is a one-way method.…”

“…For example, at 64 in 8 bit/dimension, the lattice has more than 10 nodes, and the biggest node is a pyramid number with 500 bits. The last of the aforementioned solutions was selected in [2]. Recursive formulas developed for the calculation of pyramid numbers [3] allow the use of a bisectional algorithm, originally started for each vector at a narrow border of the lattice.…”