State of the art in 2D content representation and compression

Livrable D1.3 du projet ANR PERSEECe rapport a été réalisé dans le cadre du projet ANR PERSEE (n° ANR-09-BLAN-0170). Exactement il correspond au livrable D3.1 du projet

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of Innovation (FRI) theory to the graph domain, and can be applied to arbitrary graphs via suitable approximation schemes. At its core, the introduced Graph-FRI-framework states that any K-sparse signal on the vertices of a circulant graph can be perfectly reconstructed from its dimensionality-reduced representation in the graph spectral domain, the Graph Fourier Transform (GFT), of minimum size 2K. By leveraging the recently developed theory of e-splines and e-spline wavelets on graphs, one can decompose this graph spectral transformation into the multiresolution low-pass filtering operation with a graph e-spline filter, and subsequent transformation to the spectral graph domain; this allows to infer a distinct sampling pattern, and, ultimately, the structure of an associated coarsened graph, which preserves essential properties of the original, including circularity and, where applicable, the graph generating set.Comment: To appear in Appl. Comput. Harmon. Anal. (2017

Hybrid Wavelet-Support Vector Classifiers

The Support Vector Machine (SVM) represents a new and very promising technique for machine learning tasks involving classification, regression or novelty detection. Improvements of its generalization ability can be achieved by incorporating prior knowledge of the task at hand. We propose a new hybrid algorithm consisting of signal-adapted wavelet decompositions and SVMs for waveform classification. The adaptation of the wavelet decompositions is tailormade for SVMs with radial basis functions as kernels. It allows the optimization Of the representation of the data before training the SVM and does not suffer from computationally expensive validation techniques. We assess the performance of our algorithm against the background of current concerns in medical diagnostics, namely the classification of endocardial electrograms and the detection of otoacoustic emissions. Here the performance of SVMs can significantly be improved by our adapted preprocessing step

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Exploiting parallelism within multidimensional multirate digital signal processing systems

The intense requirements for high processing rates of multidimensional Digital Signal Processing systems in practical applications justify the Application Specific Integrated Circuits designs and parallel processing implementations. In this dissertation, we propose novel theories, methodologies and architectures in designing high-performance VLSI implementations for general multidimensional multirate Digital Signal Processing systems by exploiting the parallelism within those applications. To systematically exploit the parallelism within the multidimensional multirate DSP algorithms, we develop novel transformations including (1) nonlinear I/O data space transforms, (2) intercalation transforms, and (3) multidimensional multirate unfolding transforms. These transformations are applied to the algorithms leading to systematic methodologies in high-performance architectural designs. With the novel design methodologies, we develop several architectures with parallel and distributed processing features for implementing multidimensional multirate applications. Experimental results have shown that those architectures are much more efficient in terms of execution time and/or hardware cost compared with existing hardware implementations