Uncertainty Principles and Vector Quantization

Scalar and Vector Quantization

Quantization is the process of mapping a continuous or discrete scalar or vector, produced by a source, into a set of digital symbols that can be transmitted or stored using a finite number of bits. In the case of continuous sources (with values in R or Rn) quantization must necessarily be used if the output of the source is to be communicated over a digital channel. In this case, it is, in gen...

Multiple Description Lattice Vector Quantization Multiple Description Lattice Vector Quantization

This thesis studies the multiple description vector quantization with lattice codebooks (MDLVQ). The design of index assignment is crucial to the performance of MDLVQ. However, to our best knowledge, none of previous index assignment algorithms for MDLVQ is optimal. In this thesis, we propose a simple linear-time index assignment algorithm for MDLVQ with any K ≥ 2 balanced descriptions. We prov...

Extension of two-stage vector quantization-lattice vector quantization

This paper is the extension of two-stage vector quantization–(spherical) lattice vector quantization (VQ–(S)LVQ) recently introduced by Pan and Fischer [1]. First, according to high resolution quantization theory, generalized vector quantization–lattice vector quantization (G-VQ–LVQ) is formulated in order to release the constraint of the spherical boundary for the second-stage lattice vector q...

Uncertainty principles

Traditional (West) German politics in the postwar era was very easy to understand. There were the Social Democrats (SPD) on the left, the Christian Democrats (CDU/CSU) on the right, and the much less numerous Free Democrats (FDP) in the middle. Typically, neither of the larger parties had an outright majority, so the small FDP effectively decided who could govern by choosing a coalition partner...

Vector Quantization for Image Compression-Concept Quantization