Steerable Discrete Cosine Transform

In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms

1 Comparison of Transform Coding Techniques for Two- Dimensional Arbitrarily-Shaped Images 1

Envisioned advanced multimedia video services include arbitrarily-shaped (AS) image segments as well as regular rectangular images. Images segments of the TV weather reporter produced by the chromo-key technique [1] and image segments produced by video analysis and image segmentation[2,3,4] are typical examples of AS image segments. This paper explores efficient intraframe transform coding techniques for general two-dimensional (2D) AS image segments, treating the traditional rectangular images as a special case. In particular, we focus on transform coding of the partially-defined image blocks along the boundary of the AS image segments. We recognize two different approaches — the brute-force transform coding approach and the shape-adaptive transform coding approach. The former fills up the uncovered area with the optimal redundant data such that the resulting transform spectrum is compact. A simple but efficient mirror-image extension technique is proposed. Once augmented into full image blocks, these boundary blocks can be processed by traditional block-based transform techniques like the popular Discrete Cosine Transform (DCT). In the second approach, we change either the transform basis or the coefficient calculation process adaptively based on the shape of the A

Multiple-Description Coding by Dithered Delta-Sigma Quantization

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has been fixed. Accepted for publication in the IEEE Transactions on Information Theor

Joint Unitary Triangularization for MIMO Networks

This work considers communication networks where individual links can be described as MIMO channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between sub-channels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis which is simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of sub-channel gains of two broadcast-channel receivers. We then apply this to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which only uses scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user MIMO channel, where we show the existence of non-trivial cases, where the optimal distortion pair (which for high signal-to-noise ratios equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network, thus we coin the approach "network modulation".Comment: Submitted to IEEE Tran. Signal Processing. Revised versio

Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error (MSE) distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by $R_{c}^{it}(D)$, for first-order Gauss-Markov processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze $R_{c}^{it}(D)$ for arbitrary zero-mean Gaussian stationary sources, we introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon \bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D\leq \sigma_{x}^{2}, \bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set of causal pre-, post-, and feedback filters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal filters and is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a connection to feedback quantization we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor

Robust and efficient video/image transmission

The Internet has become a primary medium for information transmission. The unreliability of channel conditions, limited channel bandwidth and explosive growth of information transmission requests, however, hinder its further development. Hence, research on robust and efficient delivery of video/image content is demanding nowadays. Three aspects of this task, error burst correction, efficient rate allocation and random error protection are investigated in this dissertation. A novel technique, called successive packing, is proposed for combating multi-dimensional (M-D) bursts of errors. A new concept of basis interleaving array is introduced. By combining different basis arrays, effective M-D interleaving can be realized. It has been shown that this algorithm can be implemented only once and yet optimal for a set of error bursts having different sizes for a given two-dimensional (2-D) array. To adapt to variable channel conditions, a novel rate allocation technique is proposed for FineGranular Scalability (FGS) coded video, in which real data based rate-distortion modeling is developed, constant quality constraint is adopted and sliding window approach is proposed to adapt to the variable channel conditions. By using the proposed technique, constant quality is realized among frames by solving a set of linear functions. Thus, significant computational simplification is achieved compared with the state-of-the-art techniques. The reduction of the overall distortion is obtained at the same time. To combat the random error during the transmission, an unequal error protection (UEP) method and a robust error-concealment strategy are proposed for scalable coded video bitstreams

Improved quality block-based low bit rate video coding.

The aim of this research is to develop algorithms for enhancing the subjective quality and coding efficiency of standard block-based video coders. In the past few years, numerous video coding standards based on motion-compensated block-transform structure have been established where block-based motion estimation is used for reducing the correlation between consecutive images and block transform is used for coding the resulting motion-compensated residual images. Due to the use of predictive differential coding and variable length coding techniques, the output data rate exhibits extreme fluctuations. A rate control algorithm is devised for achieving a stable output data rate. This rate control algorithm, which is essentially a bit-rate estimation algorithm, is then employed in a bit-allocation algorithm for improving the visual quality of the coded images, based on some prior knowledge of the images. Block-based hybrid coders achieve high compression ratio mainly due to the employment of a motion estimation and compensation stage in the coding process. The conventional bit-allocation strategy for these coders simply assigns the bits required by the motion vectors and the rest to the residual image. However, at very low bit-rates, this bit-allocation strategy is inadequate as the motion vector bits takes up a considerable portion of the total bit-rate. A rate-constrained selection algorithm is presented where an analysis-by-synthesis approach is used for choosing the best motion vectors in term of resulting bit rate and image quality. This selection algorithm is then implemented for mode selection. A simple algorithm based on the above-mentioned bit-rate estimation algorithm is developed for the latter to reduce the computational complexity. For very low bit-rate applications, it is well-known that block-based coders suffer from blocking artifacts. A coding mode is presented for reducing these annoying artifacts by coding a down-sampled version of the residual image with a smaller quantisation step size. Its applications for adaptive source/channel coding and for coding fast changing sequences are examined