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Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing (Paperback, 2010 ed.)
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Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing (Paperback, 2010 ed.)
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A long long time ago, echoing philosophical and aesthetic
principles that existed since antiquity, William of Ockham enounced
the principle of parsimony, better known today as Ockham's razor:
"Entities should not be multiplied without neces sity. " This
principle enabled scientists to select the "best" physical laws and
theories to explain the workings of the Universe and continued to
guide scienti?c research,
leadingtobeautifulresultsliketheminimaldescriptionlength
approachtostatistical inference and the related Kolmogorov
complexity approach to pattern recognition. However, notions of
complexity and description length are subjective concepts
anddependonthelanguage"spoken"whenpresentingideasandresults.
The?eldof sparse representations, that recently underwent a Big
Bang like expansion, explic itly deals with the Yin Yang interplay
between the parsimony of descriptions and the "language" or
"dictionary" used in them, and it became an extremely exciting area
of investigation. It already yielded a rich crop of mathematically
pleasing, deep and beautiful results that quickly translated into a
wealth of practical engineering applications. You are holding in
your hands the ?rst guide book to Sparseland, and I am sure you'll
?nd in it both familiar and new landscapes to see and admire, as
well as ex cellent pointers that will help you ?nd further valuable
treasures. Enjoy the journey to Sparseland! Haifa, Israel, December
2009 Alfred M. Bruckstein vii Preface This book was originally
written to serve as the material for an advanced one semester
(fourteen 2 hour lectures) graduate course for engineering students
at the Technion, Israel.
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