Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

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

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Learning-based Wavelet-like Transforms For Fully Scalable and Accessible Image Compression

The goal of this thesis is to improve the existing wavelet transform with the aid of machine learning techniques, so as to enhance coding efficiency of wavelet-based image compression frameworks, such as JPEG 2000. In this thesis, we first propose to augment the conventional base wavelet transform with two additional learned lifting steps -- a high-to-low step followed by a low-to-high step. The high-to-low step suppresses aliasing in the low-pass band by using the detail bands at the same resolution, while the low-to-high step aims to further remove redundancy from detail bands by using the corresponding low-pass band. These two additional steps reduce redundancy (notably aliasing information) amongst the wavelet subbands, and also improve the visual quality of reconstructed images at reduced resolutions. To train these two networks in an end-to-end fashion, we develop a backward annealing approach to overcome the non-differentiability of the quantization and cost functions during back-propagation. Importantly, the two additional networks share a common architecture, named a proposal-opacity topology, which is inspired and guided by a specific theoretical argument related to geometric flow. This particular network topology is compact and with limited non-linearities, allowing a fully scalable system; one pair of trained network parameters are applied for all levels of decomposition and for all bit-rates of interest. By employing the additional lifting networks within the JPEG2000 image coding standard, we can achieve up to 17.4% average BD bit-rate saving over a wide range of bit-rates, while retaining the quality and resolution scalability features of JPEG2000. Built upon the success of the high-to-low and low-to-high steps, we then study more broadly the extension of neural networks to all lifting steps that correspond to the base wavelet transform. The purpose of this comprehensive study is to understand what is the most effective way to develop learned wavelet-like transforms for highly scalable and accessible image compression. Specifically, we examine the impact of the number of learned lifting steps, the number of layers and the number of channels in each learned lifting network, and kernel support in each layer. To facilitate the study, we develop a generic training methodology that is simultaneously appropriate to all lifting structures considered. Experimental results ultimately suggest that to improve the existing wavelet transform, it is more profitable to augment a larger wavelet transform with more diverse high-to-low and low-to-high steps, rather than developing deep fully learned lifting structures

Measurements, Models, Systems and Design

531 s.

A Survey of Signal Processing Problems and Tools in Holographic Three-Dimensional Television

Cataloged from PDF version of article.Diffraction and holography are fertile areas for application of signal theory and processing. Recent work on 3DTV displays has posed particularly challenging signal processing problems. Various procedures to compute Rayleigh-Sommerfeld, Fresnel and Fraunhofer diffraction exist in the literature. Diffraction between parallel planes and tilted planes can be efficiently computed. Discretization and quantization of diffraction fields yield interesting theoretical and practical results, and allow efficient schemes compared to commonly used Nyquist sampling. The literature on computer-generated holography provides a good resource for holographic 3DTV related issues. Fast algorithms to compute Fourier, Walsh-Hadamard, fractional Fourier, linear canonical, Fresnel, and wavelet transforms, as well as optimization-based techniques such as best orthogonal basis, matching pursuit, basis pursuit etc., are especially relevant signal processing techniques for wave propagation, diffraction, holography, and related problems. Atomic decompositions, multiresolution techniques, Gabor functions, and Wigner distributions are among the signal processing techniques which have or may be applied to problems in optics. Research aimed at solving such problems at the intersection of wave optics and signal processing promises not only to facilitate the development of 3DTV systems, but also to contribute to fundamental advances in optics and signal processing theory. © 2007 IEEE

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Técnicas de compresión de imágenes hiperespectrales sobre hardware reconfigurable

Tesis de la Universidad Complutense de Madrid, Facultad de Informática, leída el 18-12-2020Sensors are nowadays in all aspects of human life. When possible, sensors are used remotely. This is less intrusive, avoids interferces in the measuring process, and more convenient for the scientist. One of the most recurrent concerns in the last decades has been sustainability of the planet, and how the changes it is facing can be monitored. Remote sensing of the earth has seen an explosion in activity, with satellites now being launched on a weekly basis to perform remote analysis of the earth, and planes surveying vast areas for closer analysis...Los sensores aparecen hoy en día en todos los aspectos de nuestra vida. Cuando es posible, de manera remota. Esto es menos intrusivo, evita interferencias en el proceso de medida, y además facilita el trabajo científico. Una de las preocupaciones recurrentes en las últimas décadas ha sido la sotenibilidad del planeta, y cómo menitoirzar los cambios a los que se enfrenta. Los estudios remotos de la tierra han visto un gran crecimiento, con satélites lanzados semanalmente para analizar la superficie, y aviones sobrevolando grades áreas para análisis más precisos...Fac. de InformáticaTRUEunpu

ICA based algorithms for computing optimal 1-D linear block transforms in variable high-rate source coding

International audienceThe Karhunen-Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources. Furthermore, under the high-resolution quantization hypothesis, nearly everything is known about the performance of a transform coding system with entropy constrained scalar quantization and mean-square distortion. It is then straightforward to find a criterion that, when minimized, gives the optimal linear transform under the abovementioned conditions. However, the optimal transform computation is generally considered as a difficult task and the Gaussian assumption is then used in order to simplify the calculus. In this paper, we present the abovementioned criterion as a contrast of independent component analysis modified by an additional term which is a penalty to non-orthogonality. Then we adapt the icainf algorithm by Pham in order to compute the transform minimizing the criterion either with no constraint or with the orthogonality constraint. Finally, experimental results show that the transforms we introduced can (1) outperform the KLT on synthetic signals, (2) achieve slightly better PSNR for high-rates and better visual quality (preservation of lines and contours) for medium-to-low rates than the KLT and 2-D DCT on grayscale natural images