This thesis investigates the problem of optimal design of binary joint watermarking and scalar quantization (JWSQ) systems that are robust under additive Gaussian attacks. A binary JWSQ system consists of two quantizers with disjoint codebooks. The joint quantization and embedding are performed by choosing the quantizer corresponding to the embedded message. The optimal JWSQ design for both fixed-rate and variable-rate cases was considered in the past, but the solution approaches exhibited high computational complexity. In this thesis, we propose faster binary JWSQ design algorithms for both the fixed-rate and variable-rate scenarios. We achieve the speed up by mapping the corresponding optimization problem to a minimum weight path problem in a certain weighted directed acyclic graph (with a constraint on the length of the path in the fixed-rate case). For this mapping to be possible we discretize the quantizer space and use an approximation for the probability of decoding error. The proposed solution algorithms have $O(LN^3)$ and $O(N^4)$ time complexity in the two cases respectively, where $N$ is the size of discretized source alphabet, and in the fixed-rate scenario $L$ is the number of cells in each quantizer. The effectiveness of the proposed designs is assessed through extensive experiments on a Gaussian source. Our results show that our algorithms are able to achieve performance very close to the prior existing schemes, but only at a small fraction of their running time. / Thesis / Master of Applied Science (MASc)

This thesis addresses the design of quantizers for two-dimensional vectors, where the scalar components are quantized sequentially. Specifically, design algorithms for unrestricted polar quantizers (UPQ) and successively refinable UPQs (SRUPQ) for vectors in polar coordinates are proposed. Additionally, algorithms for the design of sequential scalar quantizers (SSQ) for vectors with correlated components in Cartesian coordinates are devised. Both the entropy-constrained (EC) and fixed-rate (FR) cases are investigated. The proposed UPQ and SRUPQ design algorithms are developed for continuous bivariate sources with circularly symmetric densities. They are globally optimal for the class of UPQs/SRUPQs with magnitude thresholds confined to a finite set. The time complexity for the UPQ design is $O(K^2 + KP_{max})$ in the EC case, respectively $O(KN^2)$ in the FR case, where $K$ is the size of the set from which the magnitude thresholds are selected, $P_{max}$ is an upper bound for the number of phase levels corresponding to a magnitude bin, and $N$ is the total number of quantization bins. The time complexity of the SRUPQ design is $O(K^3P_{max})$ in the EC case, respectively $O(K^2N^{'2}P_{max})$ in the FR case, where $N'$ denotes the ratio between the number of bins of the fine UPQ and the coarse UPQ. The SSQ design is considered for finite-alphabet correlated sources. The proposed algorithms are globally optimal for the class of SSQs with convex cells, i.e, where each quantizer cell is the intersection of the source alphabet with an interval of the real line. The time complexity for both EC and FR cases amounts to $O(K_1^2K_2^2)$, where $K_1$ and $K_2$ are the respective sizes of the two source alphabets. It is also proved that, by applying the proposed SSQ algorithms to finite, uniform discretizations of correlated sources with continuous joint probability density function, the performance approaches that of the optimal SSQs with convex cells for the original sources as the accuracy of the discretization increases. The proposed algorithms generally rely on solving the minimum-weight path (MWP) problem in the EC case, respectively the length-constrained MWP problem or a related problem in the FR case, in a weighted directed acyclic graph (WDAG) specific to each problem. Additional computations are needed in order to evaluate the edge weights in this WDAG. In particular, in the EC-SRUPQ case, this additional work includes solving the MWP problem between multiple node pairs in some other WDAG. In the EC-SSQ (respectively, FR-SSQ) case, the additional computations consist of solving the MWP (respectively, length-constrained MWP) problem for a series of other WDAGs. / Dissertation / Doctor of Philosophy (PhD)

<p>In many scientific, medical and defense applications of image/video compression, an <em>l</em>_∞error bound is required. However, pure <em>l</em>_∞-optimized image coding, colloquially known as near-lossless image coding, is prone to structured errors such as contours and speckles if the bit rate is not sufficiently high; moreover, previous <em>l</em>_∞-based image coding methods suffer from poor rate control. In contrast, the <em>l</em>₂ error metric aims for average fidelity and hence preserves the subtlety of smooth waveforms better than the <em>l</em>_∞ error metric and it offers fine granularity in rate control; but pure <em>l</em>₂-based image coding methods (e.g., JPEG 2000) cannot bound individual errors as <em>l</em>_∞-based methods can. This thesis presents a new compression approach to retain the benefits and circumvent the pitfalls of the two error metrics.</p> / Master of Applied Science (MASc)

[pt] Em um sistema de comunicações, procura-se representar a informação gerada de forma eficiente, de modo que a redundância da informação seja reduzida ou idealmente eliminada, com o propósito de armazenamento e/ou transmissão da mesma. Este interesse justifica portanto, o estudo e desenvolvimento de técnicas de compressão que vem sendo realizado ao longo dos anos. Este trabalho de pesquisa investiga o uso de códigos de permutação para codificação de fontes segundo um critério de fidelidade, mais especificamente de fontes sem memória, caracterizadas por uma distribuição uniforme e critério de distorção de erro médio quadrático. Examina-se os códigos de permutação sob a ótica de fontes compostas e a partir desta perspectiva, apresenta-se um esquema de compressão com duplo estágio. Realiza-se então uma análise desse esquema de codificação. Faz-se também uma extensão L- dimensional (L > 1) do esquema de permutação apresentado na literatura. Os resultados obtidos comprovam um melhor desempenho da versão em duas dimensões, quando comparada ao caso unidimensional, sendo esta a principal contribuição do presente trabalho. A partir desses resultados, busca-se a aplicação de um esquema que utiliza códigos de permutação para a compressão de imagens. / [en] In communications systems the information must be represented in an efficient form, in such a way that the redundancy of the information is either reduced or ideally eliminated, with the intention of storage or transmission of the same one. This interest justifies the study and development of compression techniques that have been realized through the years. This research investigates the use of permutation codes for source encoding with a fidelity criterion, more specifically of memoryless uniform sources with mean square error fidelity criterion. We examine the permutation codes under the view of composed sources and from this perspective, a project of double stage source encoder is presented. An analysis of this project of codification is realized then. A L-dimensional extension (L > 1) of permutation codes from previous research is also introduced. The results prove a better performance of the version in two dimensions, when compared with the unidimensional case and this is the main contribution of the present study. From these results, we investigate an application for permutation codes in image compression.

<p>In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D).</p><p>In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively.</p><p>In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels.</p><p>Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity.</p><p>These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.</p>

In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D). In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively. In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels. Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity. These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.