Multiresolution Source Codes Research Articles

On the rate loss of multiresolution source codes in the Wyner-Ziv setting

In this paper, we present upper bounds on the rate loss of the multiresolution source code in the Wyner-Ziv setting (WZ-MRSC). We define two types of rate loss, the side-information rate loss and the multiresolution rate loss, to measure the nonsuccessive refinability. The former compares the rates achievable by a given WZ-MRSC to the corresponding minimal rates achievable by single-resolution Wyner-Ziv codes, and the latter refers to the difference between the rates achievable by a given WZ-MRSC and the minimal achievable rates by any WZ-MRSC at the same resolution. We bound these two types of rate loss from above and show that the side-information rate loss and corresponding successive refinability largely depend on the side information, while there exist small universal constant upper bounds on the multiresolution rate loss that are generally independent of the side information

A universal approach to queuing with distortion control

An efficient buffer-management algorithm is developed for queues that handle distortion-tolerant data under finite memory limitations. We avoid overflows and realize significant performance gains through the use of multiresolution source codes. These codes enable us to reduce the fidelity of signal descriptions in a controlled progressive manner. The proposed approach is universal, i.e., it works without knowledge of queue arrival and departure statistics. More strongly, we show that its performance is sample-path optimal, i.e., it achieves an average distortion equal to the best achievable by any algorithm, including those designed with full noncausal knowledge of queue arrival and service times.

Multiresolution Vector Quantization

Multiresolution source codes are data compression algorithms yielding embedded source descriptions. The decoder of a multiresolution code can build a source reproduction by decoding the embedded bit stream in part or in whole. All decoding procedures start at the beginning of the binary source description and decode some fraction of that string. Decoding a small portion of the binary string gives a low-resolution reproduction; decoding more yields a higher resolution reproduction; and so on. Multiresolution vector quantizers are block multiresolution source codes. This paper introduces algorithms for designing fixed- and variable-rate multiresolution vector quantizers. Experiments on synthetic data demonstrate performance close to the theoretical performance limit. Experiments on natural images demonstrate performance improvements of up to 8 dB over tree-structured vector quantizers. Some of the lessons learned through multiresolution vector quantizer design lend insight into the design of more sophisticated multiresolution codes.

Improved bounds for the rate loss of multiresolution source codes

We present new bounds for the rate loss of multiresolution source codes (MRSCs). Considering an M-resolution code, the rate loss at the ith resolution with distortion D/sub i/ is defined as L/sub i/=R/sub i/-R(D/sub i/), where R/sub i/ is the rate achievable by the MRSC at stage i. This rate loss describes the performance degradation of the MRSC compared to the best single-resolution code with the same distortion. For two-resolution source codes, there are three scenarios of particular interest: (i) when both resolutions are equally important; (ii) when the rate loss at the first resolution is 0 (L/sub 1/=0); (iii) when the rate loss at the second resolution is 0 (L/sub 2/=0). The work of Lastras and Berger (see ibid., vol.47, p.918-26, Mar. 2001) gives constant upper bounds for the rate loss of an arbitrary memoryless source in scenarios (i) and (ii) and an asymptotic bound for scenario (iii) as D/sub 2/ approaches 0. We focus on the squared error distortion measure and (a) prove that for scenario (iii) L/sub 1/<1.1610 for all D/sub 2/<D/sub 1/; (b) tighten the Lastras-Berger bound for scenario (ii) from L/sub 2//spl les/1 to L/sub 2/<0.7250; (c) tighten the Lastras-Berger bound for scenario (i) from L/sub i//spl les/1/2 to L/sub i/<0.3802, i/spl isin/{1,2}; and (d) generalize the bounds for scenarios (ii) and (iii) to M-resolution codes with M/spl ges/2. We also present upper bounds for the rate losses of additive MRSCs (AMRSCs). An AMRSC is a special MRSC where each resolution describes an incremental reproduction and the kth-resolution reconstruction equals the sum of the first k incremental reproductions. We obtain two bounds on the rate loss of AMRSCs: one primarily good for low-rate coding and another which depends on the source entropy.

Universal multiresolution source codes

A multiresolution source code is a single code giving an embedded source description that can be read at a variety of rates and thereby yields reproductions at a variety of resolutions. The resolution of a source reproduction here refers to the accuracy with which it approximates the original source. Thus, a reproduction with low distortion is a "high-resolution" reproduction while a reproduction with high distortion is a "low-resolution" reproduction. This paper treats the generalization of universal lossy source coding from single-resolution source codes to multiresolution source codes. Results described in this work include new definitions for weakly minimax universal, strongly minimax universal, and weighted universal sequences of fixed- and variable-rate multiresolution source codes that extend the corresponding notions from lossless coding and (single-resolution) quantization to multiresolution quantizers. A variety of universal multiresolution source coding results follow, including necessary and sufficient conditions for the existence of universal multiresolution codes, rate of convergence bounds for universal multiresolution coding performance to the theoretical bound, and a new multiresolution approach to two-stage universal source coding.

Distortion-rate bounds for fixed- and variable-rate multiresolution source codes

The source coding theorem for stationary sources describes the optimal performance theoretically achievable by fixed- and variable-rate block quantizers. The source coding theorem may be generalized by considering the problem of multiresolution or successive refinement source coding, which is the topic of this work. Given a distortion vector (D/sub 1/,...,D/sub L/), this work describes the family of achievable rate vectors (R/sub 1/,...,R/sub L/) for describing a stationary source at L resolutions, where the description at the first resolution is given at rate R/sub 1/ and achieves an expected distortion no greater than D/sub 1/, the description at the second resolution includes both the first description and a refining description of rate R/sub 2/ and achieves expected distortion no greater than D/sub 2/, and so on. The work includes performance bounds for both fixed- and variable-rate source codes on discrete-time stationary ergodic sources and discrete-time stationary nonergodic sources for any integer number of resolutions L/spl ges/1. For L=1, the source coding theorems for stationary sources result. For L>1, the results extend previous theorems for discrete-alphabet memoryless sources.