A fast two-stage algorithm for realizing matching pursuit

Centre for Multimedia Signal Processing, Department of Electronic and Information EngineeringVersion of RecordPublishe

Colour image coding with wavelets and matching pursuit

This thesis considers sparse approximation of still images as the basis of a lossy compression system. The Matching Pursuit (MP) algorithm is presented as a method particularly suited for application in lossy scalable image coding. Its multichannel extension, capable of exploiting inter-channel correlations, is found to be an efficient way to represent colour data in RGB colour space. Known problems with MP, high computational complexity of encoding and dictionary design, are tackled by finding an appropriate partitioning of an image. The idea of performing MP in the spatio-frequency domain after transform such as Discrete Wavelet Transform (DWT) is explored. The main challenge, though, is to encode the image representation obtained after MP into a bit-stream. Novel approaches for encoding the atomic decomposition of a signal and colour amplitudes quantisation are proposed and evaluated. The image codec that has been built is capable of competing with scalable coders such as JPEG 2000 and SPIHT in terms of compression ratio

Efficient compression of motion compensated residuals

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Toward sparse and geometry adapted video approximations

Video signals are sequences of natural images, where images are often modeled as piecewise-smooth signals. Hence, video can be seen as a 3D piecewise-smooth signal made of piecewise-smooth regions that move through time. Based on the piecewise-smooth model and on related theoretical work on rate-distortion performance of wavelet and oracle based coding schemes, one can better analyze the appropriate coding strategies that adaptive video codecs need to implement in order to be efficient. Efficient video representations for coding purposes require the use of adaptive signal decompositions able to capture appropriately the structure and redundancy appearing in video signals. Adaptivity needs to be such that it allows for proper modeling of signals in order to represent these with the lowest possible coding cost. Video is a very structured signal with high geometric content. This includes temporal geometry (normally represented by motion information) as well as spatial geometry. Clearly, most of past and present strategies used to represent video signals do not exploit properly its spatial geometry. Similarly to the case of images, a very interesting approach seems to be the decomposition of video using large over-complete libraries of basis functions able to represent salient geometric features of the signal. In the framework of video, these features should model 2D geometric video components as well as their temporal evolution, forming spatio-temporal 3D geometric primitives. Through this PhD dissertation, different aspects on the use of adaptivity in video representation are studied looking toward exploiting both aspects of video: its piecewise nature and the geometry. The first part of this work studies the use of localized temporal adaptivity in subband video coding. This is done considering two transformation schemes used for video coding: 3D wavelet representations and motion compensated temporal filtering. A theoretical R-D analysis as well as empirical results demonstrate how temporal adaptivity improves coding performance of moving edges in 3D transform (without motion compensation) based video coding. Adaptivity allows, at the same time, to equally exploit redundancy in non-moving video areas. The analogy between motion compensated video and 1D piecewise-smooth signals is studied as well. This motivates the introduction of local length adaptivity within frame-adaptive motion compensated lifted wavelet decompositions. This allows an optimal rate-distortion performance when video motion trajectories are shorter than the transformation "Group Of Pictures", or when efficient motion compensation can not be ensured. After studying temporal adaptivity, the second part of this thesis is dedicated to understand the fundamentals of how can temporal and spatial geometry be jointly exploited. This work builds on some previous results that considered the representation of spatial geometry in video (but not temporal, i.e, without motion). In order to obtain flexible and efficient (sparse) signal representations, using redundant dictionaries, the use of highly non-linear decomposition algorithms, like Matching Pursuit, is required. General signal representation using these techniques is still quite unexplored. For this reason, previous to the study of video representation, some aspects of non-linear decomposition algorithms and the efficient decomposition of images using Matching Pursuits and a geometric dictionary are investigated. A part of this investigation concerns the study on the influence of using a priori models within approximation non-linear algorithms. Dictionaries with a high internal coherence have some problems to obtain optimally sparse signal representations when used with Matching Pursuits. It is proved, theoretically and empirically, that inserting in this algorithm a priori models allows to improve the capacity to obtain sparse signal approximations, mainly when coherent dictionaries are used. Another point discussed in this preliminary study, on the use of Matching Pursuits, concerns the approach used in this work for the decompositions of video frames and images. The technique proposed in this thesis improves a previous work, where authors had to recur to sub-optimal Matching Pursuit strategies (using Genetic Algorithms), given the size of the functions library. In this work the use of full search strategies is made possible, at the same time that approximation efficiency is significantly improved and computational complexity is reduced. Finally, a priori based Matching Pursuit geometric decompositions are investigated for geometric video representations. Regularity constraints are taken into account to recover the temporal evolution of spatial geometric signal components. The results obtained for coding and multi-modal (audio-visual) signal analysis, clarify many unknowns and show to be promising, encouraging to prosecute research on the subject

Research on structure adaptive multi-atoms matching pursuit algorithm of image sparse representation

图像内容的有效表示是图像处理领域的基本问题。图像的稀疏表示是指用相对较少的数据来表示出目标图像的主要信息。稀疏表示能够更有效地对图像建模，已成为带动压缩感知与图像处理、信号处理、通信等领域发展的核心技术之一，是当前图像处理领域的研究热点与难点，受到国内外学者的广泛关注。本文主要围绕图像稀疏表示理论中过完备字典设计和快速稀疏分解算法两个方面进行了详细和深入的研究，取得的主要研究成果及创新点如下： 1)根据图像的几何结构特性，参考哺乳类动物的视觉系统感知特性，选取二维Gabor函数作为过完备字典的生成函数，建立了可以匹配多种图像结构的Gabor多成分过完备字典。该字典包含平滑、边缘轮廓与纹理三种...Efficient representation of image is the basic problem in digital image processing. Image sparse representation can capture significant information of the original image with relatively less data. Because sparse representation model can effectively represent the image, it becomes one of the core technologies which drive the development of many subjects, such as Compressed Sensing, Signal Processin...学位：工程硕士院系专业：信息科学与技术学院计算机科学系_计算机技术学号：2302009115270

非低エネルギー領域多段探索法によるMatching Pursuitsの高速化

金沢大学理工研究域電子情報学系A fast atom searching method for matching pursuits in a high-efficiency video coding system is described in this paper. The immense amount of operations is needed for the atom searching in matching pursuits, so speed-up in the searching algorithm is indispensable. We propose an atom searching algorithm that is based on both a correlation between the high signal-energy regions and optimal matching points and the correlation between the highly efficient approximated points, and to improve the computational complexity by reducing the searching points

動的学習による辞書を用いたMatching Pursuits符号化

金沢大学理工研究域電子情報学系Recently, an efficient video coding method at low bit rate using Matching Pursuits (MP) has been proposed. The MP coding method represents a signal in an approximate form using a dictionary. Therefore, coding performance depends greatly on the dictionary. In this paper, we introduce a video coding method that employs motion compensation and MP using a dynamic learning dictionary. The dictionary of the proposed method is renewed at each frame by using encoded information. Simulation results show that the coding performance of MP can be improved by applying the dynamic learning dictionary

A Geometrical Study of Matching Pursuit Parametrization

This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) geometry can be applied. The main contribution of this paper is twofold. First, we prove that if a discrete dictionary reaches a minimal density criterion, then the corresponding discrete MP (dMP) is equivalent in terms of convergence to a weakened hypothetical continuous MP. Interestingly, the corresponding weakness factor depends on a density measure of the discrete dictionary. Second, we show that the insertion of a simple geometric gradient ascent optimization on the atom dMP selection maintains the previous comparison but with a weakness factor at least two times closer to unity than without optimization. Finally, we present numerical experiments confirming our theoretical predictions for decomposition of signals and images on regular discretizations of dictionary parametrizations.Comment: 26 pages, 8 figure