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- W2953306722 abstract "We consider the minimization of the number of non-zero coefficients (the $ell_0$ norm) of the representation of a data set in terms of a dictionary under a fidelity constraint. (Both the dictionary and the norm defining the constraint are arbitrary.) This (nonconvex) optimization problem naturally leads to the sparsest representations, compared with other functionals instead of the $ell_0$ norm. Our goal is to measure the sets of data yielding a $K$-sparse solution--i.e. involving $K$ non-zero components. Data are assumed uniformly distributed on a domain defined by any norm--to be chosen by the user. A precise description of these sets of data is given and relevant bounds on the Lebesgue measure of these sets are derived. They naturally lead to bound the probability of getting a $K$-sparse solution. We also express the expectation of the number of non-zero components. We further specify these results in the case of the Euclidean norm, the dictionary being arbitrary." @default.
- W2953306722 created "2019-06-27" @default.
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- W2953306722 date "2011-01-01" @default.
- W2953306722 modified "2023-09-30" @default.
- W2953306722 title "Average performance of the sparsest approximation using a general dictionary" @default.
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