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This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary.  Apart from compressed sensing this book contains other related approaches. Each methodology has its own formalities for dealing with such problems. As an example, in the Bayesian approach, sparseness promoting priors such as Laplace and Cauchy are normally used for penalising improbable model variables, thus promoting low complexity solutions. Compressed sensing techniques and homotopy-type solutions, such as the LASSO, utilise l1-norm penalties for obtaining sparse solutions using fewer observations than conventionally needed. The book emphasizes on the role of sparsity as a machinery for promoting low complexity representations and likewise its connections to variable selection and dimensionality reduction in various engineering problems.  This book is intended for researchers, academics and practitioners with interest in various aspects and applications of sparse signal processing.  .

Signal processing --- Digital techniques --- Data processing. --- Digital techniques. --- Engineering. --- Numerical analysis. --- Algorithms. --- Complexity, Computational. --- Signal, Image and Speech Processing. --- Numeric Computing. --- Mathematics of Algorithmic Complexity. --- Complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Algorism --- Algebra --- Arithmetic --- Mathematical analysis --- Construction --- Industrial arts --- Technology --- Foundations --- Digital signal processing --- Digital communications --- Digital electronics --- Electronic data processing. --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Automation --- Signal processing. --- Image processing. --- Speech processing systems. --- Computational complexity. --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers

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Mathematics