Lower Bounds on the Redundancy of Huffman Codes with Known and Unknown Probabilities

In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where the occurrence probabilities are unknown for some of the symbols in an alphabet. Bounds can be obtained for alphabets of a given size, for alphabets of up to a given size, and for alphabets of arbitrary size. The method operates on a Computer Algebra System, yielding closed-form numbers for all results. Finally, we show the potential of the proposed method to shed some light on the structure of the minimum redundancy achievable by the Huffman code

Wireless Broadcast with Network Coding: Energy Efficiency, Optimality and Coding Gain in Lossless Wireless Networks

We consider broadcasting in multi-hop wireless networks, in which one source transmits information to all the nodes in the networks. We focus on energy efficiency, or minimizing the total number of transmissions. Our main result is the proof that, from the energy-efficiency perspective, network coding may essentially operate in an optimal way in the core of the network for uniform wireless networks in Euclidean spaces with idealized communication. In such networks, one corollary is that network coding is expected to outperform routing. We prove that the asymptotic network coding gain is comprised between 1.642 and 1.684 for networks of the plane, and comprised between 1.432 and 2.035 for networks in 3-dimensional space

Progressive transmission of pseudo-color images. Appendix 1: Item 4

The transmission of digital images can require considerable channel bandwidth. The cost of obtaining such a channel can be prohibitive, or the channel might simply not be available. In this case, progressive transmission (PT) can be useful. PT presents the user with a coarse initial image approximation, and then proceeds to refine it. In this way, the user tends to receive information about the content of the image sooner than if a sequential transmission method is used. PT finds application in image data base browsing, teleconferencing, medical and other applications. A PT scheme is developed for use with a particular type of image data, the pseudo-color or color mapped image. Such images consist of a table of colors called a colormap, plus a 2-D array of index values which indicate which colormap entry is to be used to display a given pixel. This type of image presents some unique problems for a PT coder, and techniques for overcoming these problems are developed. A computer simulation of the color mapped PT scheme is developed to evaluate its performance. Results of simulation using several test images are presented

Méthodes hybrides pour la compression d'image

Abstract : The storage and transmission of images is the basis of digital electronic communication. In order to communicate a maximum amount of information in a given period of time, one needs to look for efficient ways to represent the information communicated. Designing optimal representations is the subject of data compression. In this work, the compression methods consist of two steps in general, which are encoding and decoding. During encoding, one expresses the image by less data than the original and stores the data information; during decoding, one decodes the compressed data to show the decompressed image. In Chapter 1, we review some basic compression methods which are important in understanding the concepts of encoding and information theory as tools to build compression models and measure their efficiency. Further on, we focus on transform methods for compression, particularly we discuss in details Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT). We also analyse the hybrid method which combines DCT and DWT together to compress image data. For the sake of comparison, we discuss another total different method which is fractal image compression that compresses image data by taking advantage of self-similarity of images. We propose the hybrid method of fractal image compression and DCT based on their characteristic. Several experimental results are provided to show the outcome of the comparison between the discussed methods. This allows us to conclude that the hybrid method performs more efficiently and offers a relatively good quality of compressed image than some particular methods, but also there is some improvement can be made in the future.Le stockage et la transmission d'images sont à la base de la communication électronique numérique. Afin de communiquer un maximum d'informations dans un laps de temps donné, il faut rechercher des moyens efficaces de représenter les informations communiquées. L'objectif de base de la compression de données est la conception d'algorithmes qui permettent des représentations optimales des données. Dans ce travail, les méthodes de compression consistent en deux étapes en général, qui sont l'encodage et le décodage. Lors du codage, on exprime l'image par moins de données que l'image originale et stocke les informations obtenues; lors du décodage, on décode les données compressées pour montrer l'image décompressée. Dans le chapitre 1, nous passons en revue quelques méthodes de compression de base qui sont importantes pour comprendre les concepts d'encodage et de théorie de l'information en tant qu'outils pour construire des modèles de compression et mesurer leur efficacité. Plus loin, nous nous concentrons sur les méthodes de transformation pour la compression, en particulier nous discutons en détail des méthodes de transformée en cosinus discrète (DCT) et Transformée en ondelettes discrète (DWT). Nous analysons également la méthode hybride qui combine DCT et DWT pour compresser les données d'image. À des fins de comparaison, nous discutons d'une autre méthode totalement différente qui est la compression d'image fractale qui comprime les données d'image en tirant partie de l'autosimilarité des images. Nous proposons la méthode hybride de compression d'image fractale et DCT en fonction de leurs caractéristiques. Plusieurs résultats expérimentaux sont fournis pour montrer le résultat de la comparaison entre les méthodes discutées. Cela nous permet de conclure que la méthode hybride fonctionne plus efficacement et offre une qualité d'image compressée relativement meilleure que certaines méthodes, mais il y a aussi des améliorations qui peuvent être apportées à l'avenir

High compression image and image sequence coding

The digital representation of an image requires a very large number of bits. This number is even larger for an image sequence. The goal of image coding is to reduce this number, as much as possible, and reconstruct a faithful duplicate of the original picture or image sequence. Early efforts in image coding, solely guided by information theory, led to a plethora of methods. The compression ratio reached a plateau around 10:1 a couple of years ago. Recent progress in the study of the brain mechanism of vision and scene analysis has opened new vistas in picture coding. Directional sensitivity of the neurones in the visual pathway combined with the separate processing of contours and textures has led to a new class of coding methods capable of achieving compression ratios as high as 100:1 for images and around 300:1 for image sequences. Recent progress on some of the main avenues of object-based methods is presented. These second generation techniques make use of contour-texture modeling, new results in neurophysiology and psychophysics and scene analysis

Prioritizing Content of Interest in Multimedia Data Compression

Image and video compression techniques make data transmission and storage in digital multimedia systems more efficient and feasible for the system's limited storage and bandwidth. Many generic image and video compression techniques such as JPEG and H.264/AVC have been standardized and are now widely adopted. Despite their great success, we observe that these standard compression techniques are not the best solution for data compression in special types of multimedia systems such as microscopy videos and low-power wireless broadcast systems. In these application-specific systems where the content of interest in the multimedia data is known and well-defined, we should re-think the design of a data compression pipeline. We hypothesize that by identifying and prioritizing multimedia data's content of interest, new compression methods can be invented that are far more effective than standard techniques. In this dissertation, a set of new data compression methods based on the idea of prioritizing the content of interest has been proposed for three different kinds of multimedia systems. I will show that the key to designing efficient compression techniques in these three cases is to prioritize the content of interest in the data. The definition of the content of interest of multimedia data depends on the application. First, I show that for microscopy videos, the content of interest is defined as the spatial regions in the video frame with pixels that don't only contain noise. Keeping data in those regions with high quality and throwing out other information yields to a novel microscopy video compression technique. Second, I show that for a Bluetooth low energy beacon based system, practical multimedia data storage and transmission is possible by prioritizing content of interest. I designed custom image compression techniques that preserve edges in a binary image, or foreground regions of a color image of indoor or outdoor objects. Last, I present a new indoor Bluetooth low energy beacon based augmented reality system that integrates a 3D moving object compression method that prioritizes the content of interest.Doctor of Philosoph

Effective Method of Image Retrieval Using BTC with Gabor Wavelet Matrix

emergence of multimedia technology and the rapidly expanding image collections on the database have attracted significant research efforts in providing tools for effective retrieval and management of visual data. The need to find a desired image from a large collection. Image retrieval is the field of study concerned with searching and retrieving digital image from a collection of database .In real images, regions are often homogenous; neighboring pixels usually have similar properties (shape, color, texture). In this paper we proposed novel image retrieval based on Block Truncation Coding (BTC) with Gabor wavelet co-occurrence matrix. For image retrieval the features like shape, color, texture, spatial relation, and correlation and Eigen values are considered. BTC can be used for grayscale as well as for color images. The average precision and recall of all queries are computed and considered for performance analysis