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"Sparse modeling is a rapidly developing area at the intersection of statistical learning and signal processing, motivated by the age-old statistical problem of selecting a small number of predictive variables in high-dimensional datasets. This collection describes key approaches in sparse modeling, focusing on its applications in fields including neuroscience, computational biology, and computer vision. Sparse modeling methods can improve the interpretability of predictive models and aid efficient recovery of high-dimensional unobserved signals from a limited number of measurements. Yet despite significant advances in the field, a number of open issues remain when sparse modeling meets real-life applications. The book discusses a range of practical applications and state-of-the-art approaches for tackling the challenges presented by these applications. Topics considered include the choice of method in genomics applications; analysis of protein mass-spectrometry data; the stability of sparse models in brain imaging applications; sequential testing approaches; algorithmic aspects of sparse recovery; and learning sparse latent models"--MIT CogNet.

Sparse matrices. --- Sampling (Statistics) --- Mathematical models. --- Data reduction. --- Reduction of data --- Automatic data collection systems --- Statistics --- Models, Mathematical --- Simulation methods --- Random sampling --- Statistics of sampling --- Mathematical statistics --- Spare matrix techniques --- Matrices --- COMPUTER SCIENCE/Machine Learning & Neural Networks --- NEUROSCIENCE/General

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Sparse matrices --- Data processing --- Addresses, essays, lectures --- -Sparse matrices --- -519.6 --- 681.3*I3 --- Spare matrix techniques --- Matrices --- -Addresses, essays, lectures --- Computational mathematics. Numerical analysis. Computer programming --- Computer graphics (Computing methodologies) --- Sparse matrices. --- Data processing. --- 681.3*I3 Computer graphics (Computing methodologies) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Sparse matrices - Data processing - Addresses, essays, lectures --- Sparse matrices - Addresses, essays, lectures

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This book presents the state of the art in sparse and multiscale image and signal processing, covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Recent concepts of sparsity and morphological diversity are described and exploited for various problems such as denoising, inverse problem regularization, sparse signal decomposition, blind source separation, and compressed sensing. This book weds theory and practice in examining applications in areas such as astronomy, biology, physics, digital media, and forensics. A final chapter explores a paradigm shift in signal processing, showing that previous limits to information sampling and extraction can be overcome in very significant ways. Matlab and IDL code accompany these methods and applications to reproduce the experiments and illustrate the reasoning and methodology of the research are available for download at the associated web site.

Transformations (Mathematics) --- Signal processing. --- Image processing. --- Sparse matrices. --- Wavelets (Mathematics) --- Wavelet analysis --- Harmonic analysis --- Spare matrix techniques --- Matrices --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Algorithms --- Differential invariants --- Geometry, Differential --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing

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Numerical analysis --- Sparse matrices --- Congresses --- -519.6 --- 681.3*G13 --- Spare matrix techniques --- Matrices --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Sparse matrices - Congresses

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Sparse matrices --- Linear systems --- Matrices éparses --- Systèmes linéaires --- 519.61 --- 681.3*G13 --- Numerical methods of algebra --- Numerical linear algebra: conditioning; determinants; eigenvalues and eigenvectors; error analysis; linear systems; matrix inversion; pseudoinverses; singular value decomposition; sparse, structured, and very large systems (direct and iterative methods) --- 519.61 Numerical methods of algebra --- Matrices éparses --- Systèmes linéaires --- Spare matrix techniques --- Matrices --- Systems, Linear --- Differential equations, Linear --- System theory