Perfect reconstruction versus MMSE filter banks in source coding

Gosse, K.; Duhamel, Pierre

doi:10.1109/78.622943

Cited by 35 publications

(34 citation statements)

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“…Restricting ourselves to the class of biorthogonal FB when quantizers are present is therefore a loss of generality. A similar observation was given by Gosse and Duhamel [4] calling this more general class of filter banks minimum meansquare-error (MMSE) filter banks. Kovacevic [2] also reaches the same conclusion for the case where the subband quantizer is modeled as a Lloyd-Max quantizer.…”

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confidence: 69%

Statistically optimum pre- and postfiltering in quantization

Tuqan

Vaidyanathan²

1997

IEEE Trans. Circuits Syst. II

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Abstract-We consider the optimization of pre-and postfilters surrounding a quantization system. The goal is to optimize the filters such that the mean square error is minimized under the key constraint that the quantization noise variance is directly proportional to the variance of the quantization system input. Unlike some previous work, the postfilter is not restricted to be the inverse of the prefilter. With no order constraint on the filters, we present closed-form solutions for the optimum pre-and postfilters when the quantization system is a uniform quantizer. Using these optimum solutions, we obtain a coding gain expression for the system under study. The coding gain expression clearly indicates that, at high bit rates, there is no loss in generality in restricting the postfilter to be the inverse of the prefilter. We then repeat the same analysis with first-order preand postfilters in the form 1+z 01 and 1=(1+ z 01 ). In specific, we study two cases: 1) FIR prefilter, IIR postfilter and 2) IIR prefilter, FIR postfilter. For each case, we obtain a mean square error expression, optimize the coefficients and and provide some examples where we compare the coding gain performance with the case of = . In the last section, we assume that the quantization system is an orthonormal perfect reconstruction filter bank. To apply the optimum pre-and postfilters derived earlier, the output of the filter bank must be wide-sense stationary WSS which, in general, is not true. We provide two theorems, each under a different set of assumptions, that guarantee the wide sense stationarity of the filter bank output. We then propose a suboptimum procedure to increase the coding gain of the orthonormal filter bank.Index Terms-Half-whitening scheme, noise shaping, optimum pre-and postfiltering, subband coding.

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confidence: 69%

Statistically optimum pre- and postfiltering in quantization

Tuqan

Vaidyanathan²

1997

IEEE Trans. Circuits Syst. II

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“…Recent research has shown that reconstruction distortion can be minimized in the mean square sense (MMSE) by relaxing PR constraints and tuning the synthesis filters [154,155,156,157,158,159,160]. Naturally, mean square error minimization is of limited value for subband audio coders.…”

Section: ) Dwpt Coder With Perceptually Optimized Synthesis Waveletsmentioning

confidence: 99%

Perceptual coding of digital audio

2000

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I. INTRODUCTIONAudio coding or audio compression algorithms are used to obtain compact digital representations of high-fidelity (wideband) audio signals for the purpose of efficient transmission or storage. The central objective in audio coding is to represent the signal with a minimum number of bits while achieving transparent signal reproduction, i.e., generating output audio that cannot be distinguished from the original input, even by a sensitive listener ("golden ears"). This paper gives a review of algorithms for transparent coding of high-fidelity audio.The introduction of the compact disk (CD) in the early eighties [1] brought to the fore all of the advantages of digital audio representation, including unprecedented high-fidelity, dynamic range, and robustness. These advantages, however, came at the expense of high data rates. Conventional CD and digital audio tape (DAT) systems are typically sampled at either 44.1 or 48 kilohertz (kHz) using pulse code modulation (PCM) with a sixteen bit sample resolution. This results in uncompressed data rates of 705.6/768 kilobits per second (kbps) for a monaural channel, or 1.41/1.54 megabits per second (Mbps) for a stereo pair at 44.1/48 kHz, respectively. Although high, these data rates were accommodated successfully in first generation digital audio applications such as CD and DAT. Unfortunately, second generation multimedia applications and wireless systems in particular are often subject to bandwidth and cost constraints that are incompatible with high data rates. Because of the success enjoyed by the first generation, however, end users have come to expect "CD-quality" audio reproduction from any digital system. Therefore, new network and wireless multimedia digital audio systems must reduce data rates without compromising reproduction quality. These and other considerations have motivated considerable research during the last decade towards formulation of compression schemes that can satisfy simultaneously the conflicting demands of high compression ratios and transparent reproduction quality for high-fidelity audio signals

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“…The same idea appears in [7] with FIR filters, and is extended to the 2-D case. Further generalization is shown in [1], where general solutions are given for jointly optimizing parallel, critically sampled, synthesis filters and uniform subband quantizers. In comparison, [3] is mainly an asymptotic study of matrix Wiener filters with infinite length.…”

Section: A Connection With Previous Workmentioning

confidence: 99%

“…Section II briefly recalls the problem of optimizing a coding scheme based on parallel, critically sampled analysis filter banks with subbands of equal widths and uniform quantization [1]. In Section III, this optimization problem is modified so as to constrain the synthesis filters to be modulated versions of a low-pass prototype.…”

Section: B Outline Of the Papermentioning

confidence: 99%

“…Karp output distortion, while the synthesis bank follows directly from the choice of the analysis bank, independently of the bit-rate allocation. However, PR filter banks only provide a minimal reconstruction error when used in absence of subband quantization and previous studies already aimed at optimizing quantizers and/or the synthesis filters [1]- [10]. The approach in [1] and [10], jointly optimizes the quantizers and the synthesis filters with respect to the output mean squared error (MSE), yielding optimal (non-PR) filter banks having optimal quantization steps in the subbands, here denoted as minimum MSE (MMSE) filter banks.…”

Section: Introductionmentioning

confidence: 99%

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MMSE design of modulated and tree-structured filter banks for efficient tradeoffs between rate, distortion, and decoder complexity

Gosse

Karp

Saint-Martin³

et al. 1998

IEEE Trans. Circuits Syst. II

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Abstract-Designing filter banks for source coding purposes classically relies on perfect reconstruction filters. However, several studies have shown recently that taking the quantization noise into account in the design could yield noticeable reduction of the reconstruction distortion. In particular, a joint optimization of the synthesis filters and quantizers with respect to the output mean squared error (MSE) was proposed, and the resulting scheme was called an minimum MSE (MMSE) filter bank. However, this approach was dedicated to parallel uniform filter banks, which require a very large computational complexity. This paper is concerned with the possibility of providing MMSE filters under the constraint that the filter bank is either of a modulated or a tree-structured kind and thus of low implementation cost. Various approaches for the optimization of the synthesis bank are presented, taking into account the structural constraint. Depending on the number of parameters to be optimized, we obtain various tradeoffs between decoder complexity, transmitted bit rate, and reconstruction distortion.Index Terms-Efficient realizations, filter bank optimization, MMSE filter banks, rate-distortion optimization.

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Perfect reconstruction versus MMSE filter banks in source coding

Cited by 35 publications

References 21 publications

Statistically optimum pre- and postfiltering in quantization

Statistically optimum pre- and postfiltering in quantization

Perceptual coding of digital audio

MMSE design of modulated and tree-structured filter banks for efficient tradeoffs between rate, distortion, and decoder complexity

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