By Irina Rish
Sparse versions are fairly valuable in medical purposes, equivalent to biomarker discovery in genetic or neuroimaging facts, the place the interpretability of a predictive version is key. Sparsity may also dramatically enhance the fee potency of sign processing.
Sparse Modeling: thought, Algorithms, and Applications presents an creation to the starting to be box of sparse modeling, together with program examples, challenge formulations that yield sparse options, algorithms for locating such recommendations, and up to date theoretical effects on sparse restoration. The publication will get you in control at the most modern sparsity-related advancements and should inspire you to keep learning in regards to the field.
The authors first current motivating examples and a high-level survey of key contemporary advancements in sparse modeling. The publication then describes optimization difficulties related to commonplace sparsity-enforcing instruments, offers crucial theoretical effects, and discusses numerous state of the art algorithms for locating sparse ideas.
The authors pass directly to tackle numerous sparse restoration difficulties that stretch the elemental formula to extra refined sorts of established sparsity and to various loss capabilities. additionally they learn a selected category of sparse graphical versions and canopy dictionary studying and sparse matrix factorizations.
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Additional resources for Sparse Modeling: Theory, Algorithms, and Applications
Sample text
Surprising Empirical Results . . . . . . . . . . . . . . . . . . . . Signal Recovery from Incomplete Frequency Information . . . . . . Mutual Coherence . . . . . . . . . . . . . . . . . . . . . . . . . Spark and Uniqueness of (P0 ) Solution . . . . . . . . . . . . . . . Null Space Property and Uniqueness of (P1 ) Solution . . . . . . . . Restricted Isometry Property (RIP) .
Surprising Empirical Results . . . . . . . . . . . . . . . . . . . . Signal Recovery from Incomplete Frequency Information . . . . . . Mutual Coherence . . . . . . . . . . . . . . . . . . . . . . . . . Spark and Uniqueness of (P0 ) Solution . . . . . . . . . . . . . . . Null Space Property and Uniqueness of (P1 ) Solution . . . . . . . . Restricted Isometry Property (RIP) . . . . . . . . . . . . . . . . . Square Root Bottleneck for the Worst-Case Exact Recovery .
Summary and Bibliographical Notes . . . . . . . . . . . . . . . . 36 36 39 40 42 45 46 47 48 52 This chapter provides an overview of several theoretical results that are central to the sparse signal recovery. As already mentioned, the key questions in this field are: What types of signals can be reconstructed accurately from an incomplete set of observations? What conditions on the design matrix and on the signal would guarantee an accurate reconstruction?