Greedy vector quantization

Greedy vector quantization

We investigate the greedy version of the L-optimal vector quantization problem for an Rvalued random vector X ∈ L. We show the existence of a sequence (aN )N≥1 such that aN minimizes a 7→ ∥min1≤i≤N−1 |X−ai| ∧ |X−a| ∥∥ Lp (L-mean quantization error at level N induced by (a1, . . . , aN−1, a)). We show that this sequence produces L -rate optimal N -tuples a = (a1, . . . , aN ) (i.e. the L -mean q...

Greedy Aggregation for Vector Quantization

Abstract. Vector quantization is a classical problem that appears in many fields. Unfortunately, the quantization problem is generally non-convex, and therefore affords many local minima. The main problem is finding an initial approximation that is close to a “good” local minimum. Once such an approximation is found, the Lloyd–Max method may be used to reach a local minimum near it. In recent y...

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...

Vector Quantization for Image Compression-Concept Quantization