Based on the additive white quantization noise model, linear transform coders are derived for Gaussian sources corrupted by noise. There are two alternative design objectives: minimizing the trace of the error correla...
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Based on the additive white quantization noise model, linear transform coders are derived for Gaussian sources corrupted by noise. There are two alternative design objectives: minimizing the trace of the error correlation matrix and thus minimizing the mean-squared error, or minimizing the determinant of the error correlation matrix and thus maximizing information rate. It is shown that a solution to both problems is to first transform the noisy observations into canonical coordinates, quantize and apply a Wiener filter in this coordinate system, and then transform the result back to the original coordinates. Canonical coordinates are uncorrelated, and quantization and Wiener filtering are applied to each component independently. The type of canonical coordinate system depends on the design objective: Quantization in half-canonical coordinates minimizes the mean-squared error and quantization in full-canonical coordinates maximizes information rate. Finally, it is also demonstrated in this paper that majorization is the fundamental principle underlying proofs of optimal transform coding.
This paper reports our study on vector transform coding (VTC), a new image coding scheme, on subband-decomposed images. It is shown that vector transformation (VT) reduces the inter-vector correlation, although not as...
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This paper reports our study on vector transform coding (VTC), a new image coding scheme, on subband-decomposed images. It is shown that vector transformation (VT) reduces the inter-vector correlation, although not as much as the discrete cosine transform (DCT). However, it is also shown that VT preserves the intra-vector correlation much better than the DCT so that vector quantization (VQ) in the VT domain can be made more efficient. VTC of subband-decomposed image introduces another dimension of adaptivity, in which coding parameters, bit allocation, and VQ codebooks can be adapted to each level of the subband pyramid as well as to each vector in the VT domain. The new subband/VTC scheme is compared with VQ of original images, VQ of subband-decomposed images, DCT-based transform coding, and subband/DCT/VQ schemes. Simulation results indicate that the new scheme achieves 1 to 3dB improvement over the other schemes in terms of peak signal-to-noise ratio (PSNR). This improvement is also supported by subjective evaluations.
We extend high-rate quantization theory to Wyner-Ziv coding, i.e., lossy source coding with side information at the decoder. Ideal Slepian-Wolf coders are assumed, thus rates are conditional entropies of quantization ...
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We extend high-rate quantization theory to Wyner-Ziv coding, i.e., lossy source coding with side information at the decoder. Ideal Slepian-Wolf coders are assumed, thus rates are conditional entropies of quantization indices given the side information. This theory is applied to the analysis of orthonormal block transforms for Wyner-Ziv coding. A formula for the optimal rate allocation and an approximation to the optimal transform are derived. The case of noisy high-rate quantization and transform coding is included in our study, in which a noisy observation of source data is available at the encoder, but we are interested in estimating the unseen data at the decoder, with the help of side information. We implement a transform-domain Wyner-Ziv video coder that encodes frames independently but decodes them conditionally. Experimental results show that using the discrete cosine transform results in a rate-distortion improvement with respect to the pixel-domain coder. transform coders of noisy images for different communication constraints are compared. Experimental results show that the noisy Wyner-Ziv transform coder achieves a performance close to the case in which the side information is also available at the encoder. (c) 2006 Elsevier B.V. All rights reserved.
This paper compares the energy compacting properties of unitary transforms from transform coders and two-band paraunitary filter banks from subband coders using a cost criterion that is proposed. Stationary processes ...
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This paper compares the energy compacting properties of unitary transforms from transform coders and two-band paraunitary filter banks from subband coders using a cost criterion that is proposed. Stationary processes for which paraunitary filters have better energy compaction than unitary filters are denoted as subband optimal, and all subband optimal processes are analytically characterized for the case of length-4 filters. It is shown analytically for length-4 filters and empirically for longer-length filters that Markov-1 processes are subband optimal and that the Daubechies maximally smooth wavelet sequences achieve better energy compaction than the best unitary filters for Markov-1 inputs.
In July 2004, a new amendment called Fidelity Range Extensions (FRExt) was added to the H.264/AVC as a standardization initiative motivated by the rapidly growing demands when coding higher-fidelity video material. On...
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In July 2004, a new amendment called Fidelity Range Extensions (FRExt) was added to the H.264/AVC as a standardization initiative motivated by the rapidly growing demands when coding higher-fidelity video material. One improvement present in the FRExt is the inclusion of a new 8 x 8 integer transform that only makes use of additions and shifters to avoid mismatches between encoders and decoders. This paper presents a processor with pipeline architecture for real-time implementation of the complete process for the 8 x 8 transform coding in H.264: forward 8 x 8 integer transform, quantization and scaling, re-scaling, inverse 8 x 8 integer transform and reconstruction of the image block. This architecture has been conceived with the aim of achieving a high operation frequency and high throughput without increasing the hardware complexity. In order to achieve an efficient implementation, hardware solutions have been developed for the different circuit modules. 8 x 8 forward and inverse transforms are calculated using the separability property with architecture more suitable for pipeline schemes made up of two 1D processors and a transpose register array. New expressions for forward quantization and scaling are presented allowing efficient hardware implementation by avoiding the sign conversion. The inverse quantization has also been optimized in terms of hardware complexity by minimizing the involved arithmetic operations. Furthermore, an exhaustive analysis in the dynamic range of the datapath is made to fix the optimum bus widths with the aim of reducing the size of the circuit while avoiding overflow. Finally, the critical paths of the various computing units have been carefully analyzed and balanced using a pipeline scheme in order to maximize the operation frequency without introducing an excessive latency. A prototype with the proposed architecture has been synthesized in a 130 nm HCMOS technology process, which achieves a maximum speed of 330 MHz with a throughpu
Chain coding technique, originally developed for digital representation and processing of line drawing data, has been implemented in a transform image coding algorithm with significant performance improvement. The alg...
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Chain coding technique, originally developed for digital representation and processing of line drawing data, has been implemented in a transform image coding algorithm with significant performance improvement. The algorithm is based on the observation that the boundary of the regions of zero coefficients within a transform block can be efficiently represented by sequences of fixed line segments (chains). Preliminary results indicate significant improvements over the basic coder algorithm in which the consecutive zeros in the transform block were runlength coded. The additional implementation complexity is modest.
One of the drawbacks of the Discrete Cosine transform (DCT) is visible block boundaries due to coarse quantization of the coefficients, Most restoration techniques for the removing blocking effect are variations of lo...
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One of the drawbacks of the Discrete Cosine transform (DCT) is visible block boundaries due to coarse quantization of the coefficients, Most restoration techniques for the removing blocking effect are variations of low-pass filtering, and as such, result in unnecessary blurring of the image, In this paper, we propose a new approach for reducing the blocking effect which can be applied to conventional transform coding, such as JPEG standardized coding, without introducing additional information or significant blurring, Our technique exploits the correlation between the intensity values of boundary pixels of two neighboring blocks, Specifically, it is based on the theoretical and empirical observation that under mild assumptions, quantization of the DCT coefficients of two neighboring blocks increases the expected value of the Mean Squared Difference of Slope (MSDS) between the slope across two adjacent blocks, and the average between the boundary slopes of each of the two blocks, The amount of this increase is dependent upon the width of quantization intervals of the transform coefficients, Therefore, among all permissible inverse quantized coefficients, the set which reduces the expected value of this MSDS by an appropriate amount is most likely to decrease the blocking effect, To estimate the set of unquantized coefficients, we solve a constrained quadratic programming problem in which the quantization decision intervals provide upper and lower bound constraints on the coefficients, Our approach is based on the gradient projection method which is motivated by the ordinary method of steepest descent for unconstrained problems, Computer simulations are used to evaluate the performance of the proposed technique, We have shown that from a subjective viewpoint, the blocking effect is less noticeable in our processed images than in the ones using existing filtering techniques.
Perceptual coders have proven to be highly efficient in the context of audio or video applications involving bit rate reduction. However, this efficiency is strongly limited in very low bit rate coding conditions. Thi...
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Perceptual coders have proven to be highly efficient in the context of audio or video applications involving bit rate reduction. However, this efficiency is strongly limited in very low bit rate coding conditions. This paper studies the multiplicative effects of quantization in the frequency domain, when an overlapped filter bank (TDAC) is used to shape the quantization noise in a perceptually optimal way. The associated circular convolution operation generates aliased components in the time domain that are examined and subjected to minimization. A closed form expression is suggested to approximate an optimal transform window offering a desired tradeoff between the reduction of the time artifacts produced by a coarse quantization and the reduction of the stop-band leakage, relative to other transform windows commonly used.
We review a class of methods that can be collected under the name nonlinear transform coding (NTC), which over the past few years have become competitive with the best linear transform codecs for images, and have supe...
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We review a class of methods that can be collected under the name nonlinear transform coding (NTC), which over the past few years have become competitive with the best linear transform codecs for images, and have superseded them in terms of rate-distortion performance under established perceptual quality metrics such as MS-SSIM. We assess the empirical rate-distortion performance of NTC with the help of simple example sources, for which the optimal performance of a vector quantizer is easier to estimate than with natural data sources. To this end, we introduce a novel variant of entropy-constrained vector quantization. We provide an analysis of various forms of stochastic optimization techniques for NTC models;review architectures of transforms based on artificial neural networks, as well as learned entropy models;and provide a direct comparison of a number of methods to parameterize the rate-distortion trade-off of nonlinear transforms, introducing a simplified one.
Motion-compensated interframe transform coding has been recommended as an efficient method of coding image sequences at low bit rates. The paper considers the effect of employing a variety of different transform and m...
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Motion-compensated interframe transform coding has been recommended as an efficient method of coding image sequences at low bit rates. The paper considers the effect of employing a variety of different transform and motion compensation techniques on the operation of the algorithm and also the interrelation between the predictive and transform parts of the scheme in terms of the spectral properties of the signal to be transformed. It is shown that, for a wide variety of source material, there is a complex interaction between the specific transform and motion compensation scheme employed, and that the efficiency of the motion-compensated predictive operation strongly influences the performance of the subsequent transform step.
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