Alternative formulations for bit allocation with dependent quantization

Batra, Pankaj; Eleftheriadis, Alexandros

doi:10.1109/icassp.2002.5745410

Cited by 3 publications

(5 citation statements)

References 26 publications

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“…By deriving the statistical and rate-distortion characteristics of different components of the interframe problem we showed that the set of optimal breakpoint values for any frame is somewhat invariant to the accumulated motion compensated shaping error from past frames and may be very reasonably approximated using the current frame shaping error alone. This result is significant because it opens up the way to construct simpler memoryless algorithms that give minimal penalty in achieved picture quality, not just for this, but possibly other types of problems such as those in [1], [6], [7], and [34]. Rate shaping is directly applicable to traditional codecs such as H.261, H.263, MPEG-1, MPEG-2, and MPEG-4.…”

Section: Discussionmentioning

confidence: 91%

“…The interested reader may refer to [19] for a detailed description of the Lagrangian relaxation algorithm. Note that since the selection set is discrete in nature, the above Integer Problem (IP) [39] may alternatively be relaxed to a linear program [6], [7], [9]. This approach has been well studied in similar problem setups [5] and is known to perform very close to IP optimality in time that is linear in the size of the optimization window.…”

Section: B Constrained Drs Of Intracoded Picturesmentioning

confidence: 96%

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Dynamic rate shaping of compressed digital video

Eleftheriadis

Batra

2006

IEEE Trans. Multimedia

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We discuss new theoretical and experimental results on the dynamic rate shaping (DRS) approach for transcoding compressed video bitstreams (MPEG-1, MPEG-2, MPEG-4, H.261, as well as JPEG). We analyze the behavior of DRS assuming a first order autoregressive source. We propose a set of low complexity algorithms for both constrained and unconstrained DRS and substantiate the almost-optimal experimental performance of the memoryless algorithm by assuming a first order autoregressive source. By deriving the statistical and rate-distortion characteristics of different components of the interframe rate shaping problem, we offer an explanation as to why the set of optimal breakpoint values for any frame is somewhat invariant to the accumulated motion compensated shaping error from past frames. We also present an extensive experimental study on the various DRS algorithms (causally optimal, memoryless, and rate-based) both in their constrained and generalized forms. The study proves the computational viability of the DRS approach to transcoding and identifies a range of rate shaping ratios for which it is better than requantization, both complexity-wise as well as in performance. This result is significant in that it opens up the way to construct much simpler memoryless algorithms that give minimal penalty in achieved quality, not just for this but possibly other types of algorithms. This is also the very first use of matrix perturbation theory for tracking the spectral behavior of the autocorrelation matrix of the source signal and the motion residual it yields.

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Section: Discussionmentioning

confidence: 91%

Section: B Constrained Drs Of Intracoded Picturesmentioning

confidence: 96%

Dynamic rate shaping of compressed digital video

Eleftheriadis

Batra

2006

IEEE Trans. Multimedia

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“…We will assume the MSE of the th quantizer is equal to (1) where is a quantity dependent on the distribution of , but independent of . It is known that (1) is satisfied for asymptotically optimal scalar quantization [14], in which case where denotes the probability density function of .…”

Section: Letmentioning

confidence: 99%

“…Fox [12] gave a greedy algorithm for finding nonnegative integer bit allocations by allocating one bit at a time to a set of quantizers. His algorithm is optimal for any convex decreasing distortion function, and in particular, it is optimal for the distortion function we assume in (1).…”

Section: Equivalence Of Closest Nonnegative Integer Bit Allocationmentioning

confidence: 99%

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Quantization of Multiple Sources Using Nonnegative Integer Bit Allocation

Farber

Zeger

2006

IEEE Trans. Inform. Theory

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Asymptotically optimal real-valued bit allocation among a set of quantizers for a finite collection of sources was derived in 1963 by Huang and Schultheiss, and an algorithm for obtaining an optimal nonnegative integer-valued bit allocation was given by Fox in 1966. We prove that, for a given bit budget, the set of optimal nonnegative integer-valued bit allocations is equal to the set of nonnegative integer-valued bit allocation vectors which minimize the Euclidean distance to the optimal real-valued bit-allocation vector of Huang and Schultheiss. We also give an algorithm for finding optimal nonnegative integer-valued bit allocations. The algorithm has lower computational complexity than Fox's algorithm, as the bit budget grows. Finally, we compare the performance of the Huang-Schultheiss solution to that of an optimal integer-valued bit allocation. Specifically, we derive upper and lower bounds on the deviation of the mean-squared error (MSE) using optimal integer-valued bit allocation from the MSE using optimal real-valued bit allocation. It is shown that, for asymptotically large transmission rates, optimal integer-valued bit allocations do not necessarily achieve the same performance as that predicted by Huang-Schultheiss for optimal real-valued bit allocations.

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