Universal Quantization for Separate Encodings and Joint Decoding of Correlated Sources

We consider the multi-user lossy source-coding problem for continuous alphabet sources. In a previous work, Ziv proposed a single-user universal coding scheme which uses uniform quantization with dither, followed by a lossless source encoder (entropy coder). In this paper, we generalize Ziv's scheme to the multi-user setting. For this generalized universal scheme, upper bounds are derived on the redundancies, defined as the differences between the actual rates and the closest corresponding rates on the boundary of the rate region. It is shown that this scheme can achieve redundancies of no more than 0.754 bits per sample for each user. These bounds are obtained without knowledge of the multi-user rate region, which is an open problem in general. As a direct consequence of these results, inner and outer bounds on the rate-distortion achievable region are obtained.Comment: 24 pages, 1 figur

Incremental Refinements and Multiple Descriptions with Feedback

It is well known that independent (separate) encoding of K correlated sources may incur some rate loss compared to joint encoding, even if the decoding is done jointly. This loss is particularly evident in the multiple descriptions problem, where the sources are repetitions of the same source, but each description must be individually good. We observe that under mild conditions about the source and distortion measure, the rate ratio Rindependent(K)/Rjoint goes to one in the limit of small rate/high distortion. Moreover, we consider the excess rate with respect to the rate-distortion function, Rindependent(K, M) - R(D), in M rounds of K independent encodings with a final distortion level D. We provide two examples - a Gaussian source with mean-squared error and an exponential source with one-sided error - for which the excess rate vanishes in the limit as the number of rounds M goes to infinity, for any fixed D and K. This result has an interesting interpretation for a multi-round variant of the multiple descriptions problem, where after each round the encoder gets a (block) feedback regarding which of the descriptions arrived: In the limit as the number of rounds M goes to infinity (i.e., many incremental rounds), the total rate of received descriptions approaches the rate-distortion function. We provide theoretical and experimental evidence showing that this phenomenon is in fact more general than in the two examples above.Comment: 62 pages. Accepted in the IEEE Transactions on Information Theor

Algorithms for compression of high dynamic range images and video

The recent advances in sensor and display technologies have brought upon the High Dynamic Range (HDR) imaging capability. The modern multiple exposure HDR sensors can achieve the dynamic range of 100-120 dB and LED and OLED display devices have contrast ratios of 10^5:1 to 10^6:1. Despite the above advances in technology the image/video compression algorithms and associated hardware are yet based on Standard Dynamic Range (SDR) technology, i.e. they operate within an effective dynamic range of up to 70 dB for 8 bit gamma corrected images. Further the existing infrastructure for content distribution is also designed for SDR, which creates interoperability problems with true HDR capture and display equipment. The current solutions for the above problem include tone mapping the HDR content to fit SDR. However this approach leads to image quality associated problems, when strong dynamic range compression is applied. Even though some HDR-only solutions have been proposed in literature, they are not interoperable with current SDR infrastructure and are thus typically used in closed systems. Given the above observations a research gap was identified in the need for efficient algorithms for the compression of still images and video, which are capable of storing full dynamic range and colour gamut of HDR images and at the same time backward compatible with existing SDR infrastructure. To improve the usability of SDR content it is vital that any such algorithms should accommodate different tone mapping operators, including those that are spatially non-uniform. In the course of the research presented in this thesis a novel two layer CODEC architecture is introduced for both HDR image and video coding. Further a universal and computationally efficient approximation of the tone mapping operator is developed and presented. It is shown that the use of perceptually uniform colourspaces for internal representation of pixel data enables improved compression efficiency of the algorithms. Further proposed novel approaches to the compression of metadata for the tone mapping operator is shown to improve compression performance for low bitrate video content. Multiple compression algorithms are designed, implemented and compared and quality-complexity trade-offs are identified. Finally practical aspects of implementing the developed algorithms are explored by automating the design space exploration flow and integrating the high level systems design framework with domain specific tools for synthesis and simulation of multiprocessor systems. The directions for further work are also presented

A study of data coding technology developments in the 1980-1985 time frame, volume 2

The source parameters of digitized analog data are discussed. Different data compression schemes are outlined and analysis of their implementation are presented. Finally, bandwidth compression techniques are given for video signals

Design Techniques for Energy-Quality Scalable Digital Systems

Energy efficiency is one of the key design goals in modern computing. Increasingly complex tasks are being executed in mobile devices and Internet of Things end-nodes, which are expected to operate for long time intervals, in the orders of months or years, with the limited energy budgets provided by small form-factor batteries. Fortunately, many of such tasks are error resilient, meaning that they can toler- ate some relaxation in the accuracy, precision or reliability of internal operations, without a significant impact on the overall output quality. The error resilience of an application may derive from a number of factors. The processing of analog sensor inputs measuring quantities from the physical world may not always require maximum precision, as the amount of information that can be extracted is limited by the presence of external noise. Outputs destined for human consumption may also contain small or occasional errors, thanks to the limited capabilities of our vision and hearing systems. Finally, some computational patterns commonly found in domains such as statistics, machine learning and operational research, naturally tend to reduce or eliminate errors. Energy-Quality (EQ) scalable digital systems systematically trade off the quality of computations with energy efficiency, by relaxing the precision, the accuracy, or the reliability of internal software and hardware components in exchange for energy reductions. This design paradigm is believed to offer one of the most promising solutions to the impelling need for low-energy computing. Despite these high expectations, the current state-of-the-art in EQ scalable design suffers from important shortcomings. First, the great majority of techniques proposed in literature focus only on processing hardware and software components. Nonetheless, for many real devices, processing contributes only to a small portion of the total energy consumption, which is dominated by other components (e.g. I/O, memory or data transfers). Second, in order to fulfill its promises and become diffused in commercial devices, EQ scalable design needs to achieve industrial level maturity. This involves moving from purely academic research based on high-level models and theoretical assumptions to engineered flows compatible with existing industry standards. Third, the time-varying nature of error tolerance, both among different applications and within a single task, should become more central in the proposed design methods. This involves designing “dynamic” systems in which the precision or reliability of operations (and consequently their energy consumption) can be dynamically tuned at runtime, rather than “static” solutions, in which the output quality is fixed at design-time. This thesis introduces several new EQ scalable design techniques for digital systems that take the previous observations into account. Besides processing, the proposed methods apply the principles of EQ scalable design also to interconnects and peripherals, which are often relevant contributors to the total energy in sensor nodes and mobile systems respectively. Regardless of the target component, the presented techniques pay special attention to the accurate evaluation of benefits and overheads deriving from EQ scalability, using industrial-level models, and on the integration with existing standard tools and protocols. Moreover, all the works presented in this thesis allow the dynamic reconfiguration of output quality and energy consumption. More specifically, the contribution of this thesis is divided in three parts. In a first body of work, the design of EQ scalable modules for processing hardware data paths is considered. Three design flows are presented, targeting different technologies and exploiting different ways to achieve EQ scalability, i.e. timing-induced errors and precision reduction. These works are inspired by previous approaches from the literature, namely Reduced-Precision Redundancy and Dynamic Accuracy Scaling, which are re-thought to make them compatible with standard Electronic Design Automation (EDA) tools and flows, providing solutions to overcome their main limitations. The second part of the thesis investigates the application of EQ scalable design to serial interconnects, which are the de facto standard for data exchanges between processing hardware and sensors. In this context, two novel bus encodings are proposed, called Approximate Differential Encoding and Serial-T0, that exploit the statistical characteristics of data produced by sensors to reduce the energy consumption on the bus at the cost of controlled data approximations. The two techniques achieve different results for data of different origins, but share the common features of allowing runtime reconfiguration of the allowed error and being compatible with standard serial bus protocols. Finally, the last part of the manuscript is devoted to the application of EQ scalable design principles to displays, which are often among the most energy- hungry components in mobile systems. The two proposals in this context leverage the emissive nature of Organic Light-Emitting Diode (OLED) displays to save energy by altering the displayed image, thus inducing an output quality reduction that depends on the amount of such alteration. The first technique implements an image-adaptive form of brightness scaling, whose outputs are optimized in terms of balance between power consumption and similarity with the input. The second approach achieves concurrent power reduction and image enhancement, by means of an adaptive polynomial transformation. Both solutions focus on minimizing the overheads associated with a real-time implementation of the transformations in software or hardware, so that these do not offset the savings in the display. For each of these three topics, results show that the aforementioned goal of building EQ scalable systems compatible with existing best practices and mature for being integrated in commercial devices can be effectively achieved. Moreover, they also show that very simple and similar principles can be applied to design EQ scalable versions of different system components (processing, peripherals and I/O), and to equip these components with knobs for the runtime reconfiguration of the energy versus quality tradeoff

Learning to compress and search visual data in large-scale systems

The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and hence the model capacity can be controlled. The algorithmic infrastructure is developed based on the synthesis and analysis prior models whose rate-distortion properties, as well as capacity vs. sample complexity trade-offs are carefully optimized. These models are then extended to multi-layers, namely the RRQ and the ML-STC frameworks, where the latter is further evolved as a powerful deep neural network architecture with fast and sample-efficient training and discrete representations. For the developed algorithms, three important applications are developed. First, the problem of large-scale similarity search in retrieval systems is addressed, where a double-stage solution is proposed leading to faster query times and shorter database storage. Second, the problem of learned image compression is targeted, where the proposed models can capture more redundancies from the training images than the conventional compression codecs. Finally, the proposed algorithms are used to solve ill-posed inverse problems. In particular, the problems of image denoising and compressive sensing are addressed with promising results.Comment: PhD thesis dissertatio

Online Multi-Stage Deep Architectures for Feature Extraction and Object Recognition

Multi-stage visual architectures have recently found success in achieving high classification accuracies over image datasets with large variations in pose, lighting, and scale. Inspired by techniques currently at the forefront of deep learning, such architectures are typically composed of one or more layers of preprocessing, feature encoding, and pooling to extract features from raw images. Training these components traditionally relies on large sets of patches that are extracted from a potentially large image dataset. In this context, high-dimensional feature space representations are often helpful for obtaining the best classification performances and providing a higher degree of invariance to object transformations. Large datasets with high-dimensional features complicate the implementation of visual architectures in memory constrained environments. This dissertation constructs online learning replacements for the components within a multi-stage architecture and demonstrates that the proposed replacements (namely fuzzy competitive clustering, an incremental covariance estimator, and multi-layer neural network) can offer performance competitive with their offline batch counterparts while providing a reduced memory footprint. The online nature of this solution allows for the development of a method for adjusting parameters within the architecture via stochastic gradient descent. Testing over multiple datasets shows the potential benefits of this methodology when appropriate priors on the initial parameters are unknown. Alternatives to batch based decompositions for a whitening preprocessing stage which take advantage of natural image statistics and allow simple dictionary learners to work well in the problem domain are also explored. Expansions of the architecture using additional pooling statistics and multiple layers are presented and indicate that larger codebook sizes are not the only step forward to higher classification accuracies. Experimental results from these expansions further indicate the important role of sparsity and appropriate encodings within multi-stage visual feature extraction architectures

Rate Distortion Theory for Causal Video Coding: Characterization, Computation Algorithm, Comparison, and Code Design

Due to the sheer volume of data involved, video coding is an important application of lossy source coding, and has received wide industrial interest and support as evidenced by the development and success of a series of video coding standards. All MPEG-series and H-series video coding standards proposed so far are based upon a video coding paradigm called predictive video coding, where video source frames Xᵢ,i=1,2,...,N, are encoded in a frame by frame manner, the encoder and decoder for each frame Xᵢ, i =1, 2, ..., N, enlist help only from all previous encoded frames Sj, j=1, 2, ..., i-1. In this thesis, we will look further beyond all existing and proposed video coding standards, and introduce a new coding paradigm called causal video coding, in which the encoder for each frame Xᵢ can use all previous original frames Xj, j=1, 2, ..., i-1, and all previous encoded frames Sj, while the corresponding decoder can use only all previous encoded frames. We consider all studies, comparisons, and designs on causal video coding from an information theoretic point of view. Let R*c(D₁,...,D_N) (R*p(D₁,...,D_N), respectively) denote the minimum total rate required to achieve a given distortion level D₁,...,D_N > 0 in causal video coding (predictive video coding, respectively). A novel computation approach is proposed to analytically characterize, numerically compute, and compare the minimum total rate of causal video coding R*c(D₁,...,D_N) required to achieve a given distortion (quality) level D₁,...,D_N > 0. Specifically, we first show that for jointly stationary and ergodic sources X₁, ..., X_N, R*c(D₁,...,D_N) is equal to the infimum of the n-th order total rate distortion function R_{c,n}(D₁,...,D_N) over all n, where R_{c,n}(D₁,...,D_N) itself is given by the minimum of an information quantity over a set of auxiliary random variables. We then present an iterative algorithm for computing R_{c,n}(D₁,...,D_N) and demonstrate the convergence of the algorithm to the global minimum. The global convergence of the algorithm further enables us to not only establish a single-letter characterization of R*c(D₁,...,D_N) in a novel way when the N sources are an independent and identically distributed (IID) vector source, but also demonstrate a somewhat surprising result (dubbed the more and less coding theorem)---under some conditions on source frames and distortion, the more frames need to be encoded and transmitted, the less amount of data after encoding has to be actually sent. With the help of the algorithm, it is also shown by example that R*c(D₁,...,D_N) is in general much smaller than the total rate offered by the traditional greedy coding method by which each frame is encoded in a local optimum manner based on all information available to the encoder of the frame. As a by-product, an extended Markov lemma is established for correlated ergodic sources. From an information theoretic point of view, it is interesting to compare causal video coding and predictive video coding, which all existing video coding standards proposed so far are based upon. In this thesis, by fixing N=3, we first derive a single-letter characterization of R*p(D₁,D₂,D₃) for an IID vector source (X₁,X₂,X₃) where X₁ and X₂ are independent, and then demonstrate the existence of such X₁,X₂,X₃ for which R*p(D₁,D₂,D₃)>R*c(D₁,D₂,D₃) under some conditions on source frames and distortion. This result makes causal video coding an attractive framework for future video coding systems and standards. The design of causal video coding is also considered in the thesis from an information theoretic perspective by modeling each frame as a stationary information source. We first put forth a concept called causal scalar quantization, and then propose an algorithm for designing optimum fixed-rate causal scalar quantizers for causal video coding to minimize the total distortion among all sources. Simulation results show that in comparison with fixed-rate predictive scalar quantization, fixed-rate causal scalar quantization offers as large as 16% quality improvement (distortion reduction)