Coding overcomplete representations of audio using the MCLT

We propose a system for audio coding using the modulated complex lapped transform (MCLT). In general, it is difficult to encode signals using overcomplete representations without avoiding a penalty in rate-distortion performance. We show that the penalty can be significantly reduced for MCLT-based representations, without the need for iterative methods of sparsity reduction. We achieve that via a magnitude-phase polar quantization and the use of magnitude and phase prediction. Compared to systems based on quantization of orthogonal representations such as the modulated lapped transform (MLT), the new system allows for reduced warbling artifacts and more precise computation of frequency-domain auditory masking functions

Image Coding based Orthogonal Polynomials Multiresolution Analysis with Joint Probability Context Modeling and Modified Golomb-Rice Entropy Coding

The work proposes, a JPEG2000 like compression technique which is  based on multiresolution analysis of orthogonal polynomials transformation (OPT)  coefficients has been presented with bit modeling for Golomb-Rice entropy coding. Initially, the image under analysis is divided into blocks and OPT is applied to each divided blocks. Then, transformed coefficients are represented as sub bands like structure (multiresolution) and scalar quantization is carried out to the transformed coefficients to reduce the precision. The quantized coefficients are then bit modelled in the bit plane using a joint probability statistical model, and significant bits in the bit plane are chosen. On the selected relevant bits, a geometrically distributed set of context is modelled for further encoding with modified Golomb-Rice encoding to provide compressed data. The decompression procedure is just the reverse of compression procedure. Experiments and analysis are carried out to demonstrate the efficiency of the proposed compression scheme in terms of compression ratio and Peak-Signal-to Noise Ratio (PSNR), and the results are encouragin

New Classes of Random Sequences for Coding and Cryptography Applications

Cryptography is required for securing data in a digital or analog medium and there exists a variety of protocols to encode the data and decrypt them without third party interference. Random numbers must be used to generate keys so that they cannot be guessed easily. This thesis investigates new classes of random numbers, including Gopala-Hemachandra (GH) and Narayana sequences, which are variants of the well-known Fibonacci sequences. Various mathematical properties of GH and Narayana sequences modulo prime have been found including their periods. Considering GH sequences modulo prime p, the periods are shown to be either (p-1) (or a divisor) or (2p+2) (or a divisor) while the Narayana sequence for prime modulo have either p2+p+1 (or a divisor) or p2-1 (or a divisor) as their periods. New results on the use of the Narayana sequence as a universal code have been obtained.It is shown that the autocorrelation and cross correlation properties of GH and Narayana sequences justify their use as random sequences. The signal to noise ratio values are calculated based on the use of delayed sequences to carry different sets of data in wireless applications. The thesis shows that GH and Narayana sequences are suitable for many encoding and decoding applications including key generation and securing transmission of data.Electrical Engineerin

Graph Signal Processing:Sparse Representation and Applications

Over the past few decades we have been experiencing an explosion of information generated by large networks of sensors and other data sources. Much of this data is intrinsically structured, such as traffic evolution in a transportation network, temperature values in different geographical locations, information diffusion in social networks, functional activities in the brain, or 3D meshes in computer graphics. The representation, analysis, and compression of such data is a challenging task and requires the development of new tools that can identify and properly exploit the data structure. In this thesis, we formulate the processing and analysis of structured data using the emerging framework of graph signal processing. Graphs are generic data representation forms, suitable for modeling the geometric structure of signals that live on topologically complicated domains. The vertices of the graph represent the discrete data domain, and the edge weights capture the pairwise relationships between the vertices. A graph signal is then defined as a function that assigns a real value to each vertex. Graph signal processing is a useful framework for handling efficiently such data as it takes into consideration both the signal and the graph structure. In this work, we develop new methods and study several important problems related to the representation and structure-aware processing of graph signals in both centralized and distributed settings. We focus in particular in the theory of sparse graph signal representation and its applications and we bring some insights towards better understanding the interplay between graphs and signals on graphs. First, we study a novel yet natural application of the graph signal processing framework for the representation of 3D point cloud sequences. We exploit graph-based transform signal representations for addressing the challenging problem of compression of data that is characterized by dynamic 3D positions and color attributes. Next, we depart from graph-based transform signal representations to design new overcomplete representations, or dictionaries, which are adapted to specific classes of graph signals. In particular, we address the problem of sparse representation of graph signals residing on weighted graphs by learning graph structured dictionaries that incorporate the intrinsic geometric structure of the irregular data domain and are adapted to the characteristics of the signals. Then, we move to the efficient processing of graph signals in distributed scenarios, such as sensor or camera networks, which brings important constraints in terms of communication and computation in realistic settings. In particular, we study the effect of quantization in the distributed processing of graph signals that are represented by graph spectral dictionaries and we show that the impact of the quantization depends on the graph geometry and on the structure of the spectral dictionaries. Finally, we focus on a widely used graph process, the problem of distributed average consensus in a sensor network where sensors exchange quantized information with their neighbors. We propose a novel quantization scheme that depends on the graph topology and exploits the increasing correlation between the values exchanged by the sensors throughout the iterations of the consensus algorithm

Techniques of design optimisation for algorithms implemented in software

The overarching objective of this thesis was to develop tools for parallelising, optimising, and implementing algorithms on parallel architectures, in particular General Purpose Graphics Processors (GPGPUs). Two projects were chosen from different application areas in which GPGPUs are used: a defence application involving image compression, and a modelling application in bioinformatics (computational immunology). Each project had its own specific objectives, as well as supporting the overall research goal. The defence / image compression project was carried out in collaboration with the Jet Propulsion Laboratories. The specific questions were: to what extent an algorithm designed for bit-serial for the lossless compression of hyperspectral images on-board unmanned vehicles (UAVs) in hardware could be parallelised, whether GPGPUs could be used to implement that algorithm, and whether a software implementation with or without GPGPU acceleration could match the throughput of a dedicated hardware (FPGA) implementation. The dependencies within the algorithm were analysed, and the algorithm parallelised. The algorithm was implemented in software for GPGPU, and optimised. During the optimisation process, profiling revealed less than optimal device utilisation, but no further optimisations resulted in an improvement in speed. The design had hit a local-maximum of performance. Analysis of the arithmetic intensity and data-flow exposed flaws in the standard optimisation metric of kernel occupancy used for GPU optimisation. Redesigning the implementation with revised criteria (fused kernels, lower occupancy, and greater data locality) led to a new implementation with 10x higher throughput. GPGPUs were shown to be viable for on-board implementation of the CCSDS lossless hyperspectral image compression algorithm, exceeding the performance of the hardware reference implementation, and providing sufficient throughput for the next generation of image sensor as well. The second project was carried out in collaboration with biologists at the University of Arizona and involved modelling a complex biological system – VDJ recombination involved in the formation of T-cell receptors (TCRs). Generation of immune receptors (T cell receptor and antibodies) by VDJ recombination is an enormously complex process, which can theoretically synthesize greater than 1018 variants. Originally thought to be a random process, the underlying mechanisms clearly have a non-random nature that preferentially creates a small subset of immune receptors in many individuals. Understanding this bias is a longstanding problem in the field of immunology. Modelling the process of VDJ recombination to determine the number of ways each immune receptor can be synthesized, previously thought to be untenable, is a key first step in determining how this special population is made. The computational tools developed in this thesis have allowed immunologists for the first time to comprehensively test and invalidate a longstanding theory (convergent recombination) for how this special population is created, while generating the data needed to develop novel hypothesis

Depth-Map Image Compression Based on Region and Contour Modeling

In this thesis, the problem of depth-map image compression is treated. The compilation of articles included in the thesis provides methodological contributions in the fields of lossless and lossy compression of depth-map images.The first group of methods addresses the lossless compression problem. The introduced methods are using the approach of representing the depth-map image in terms of regions and contours. In the depth-map image, a segmentation defines the regions, by grouping pixels having similar properties, and separates them using (region) contours. The depth-map image is encoded by the contours and the auxiliary information needed to reconstruct the depth values in each region.One way of encoding the contours is to describe them using two matrices of horizontal and vertical contour edges. The matrices are encoded using template context coding where each context tree is optimally pruned. In certain contexts, the contour edges are found deterministically using only the currently available information. Another way of encoding the contours is to describe them as a sequence of contour segments. Each such segment is defined by an anchor (starting) point and a string of contour edges, equivalent to a string of chain-code symbols. Here we propose efficient ways to select and encode the anchor points and to generate contour segments by using a contour crossing point analysis and by imposing rules that help in minimizing the number of anchor points.The regions are reconstructed at the decoder using predictive coding or the piecewise constant model representation. In the first approach, the large constant regions are found and one depth value is encoded for each such region. For the rest of the image, suitable regions are generated by constraining the local variation of the depth level from one pixel to another. The nonlinear predictors selected specifically for each region are combining the results of several linear predictors, each fitting optimally a subset of pixels belonging to the local neighborhood. In the second approach, the depth value of a given region is encoded using the depth values of the neighboring regions already encoded. The natural smoothness of the depth variation and the mutual exclusiveness of the values in neighboring regions are exploited to efficiently predict and encode the current region's depth value.The second group of methods is studying the lossy compression problem. In a first contribution, different segmentations are generated by varying the threshold for the depth local variability. A lossy depth-map image is obtained for each segmentation and is encoded based on predictive coding, quantization and context tree coding. In another contribution, the lossy versions of one image are created either by successively merging the constant regions of the original image, or by iteratively splitting the regions of a template image using horizontal or vertical line segments. Merging and splitting decisions are greedily taken, according to the best slope towards the next point in the rate-distortion curve. An entropy coding algorithm is used to encode each image.We propose also a progressive coding method for coding the sequence of lossy versions of a depth-map image. The bitstream is encoded so that any lossy version of the original image is generated, starting from a very low resolution up to lossless reconstruction. The partitions of the lossy versions into regions are assumed to be nested so that a higher resolution image is obtained by splitting some regions of a lower resolution image. A current image in the sequence is encoded using the a priori information from a previously encoded image: the anchor points are encoded relative to the already encoded contour points; the depth information of the newly resulting regions is recovered using the depth value of the parent region.As a final contribution, the dissertation includes a study of the parameterization of planar models. The quantized heights at three-pixel locations are used to compute the optimal plane for each region. The three-pixel locations are selected so that the distortion due to the approximation of the plane over the region is minimized. The planar model and the piecewise constant model are competing in the merging process, where the two regions to be merged are those ensuring the optimal slope in the rate-distortion curve