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- W2792925054 abstract "Motivated by the observation that a given signal x may admit sparse representations in multiple dictionaries Ψ d , but with varying levels of sparsity across dictionaries, we propose two new algorithms for signal reconstruction from noisy linear measurements. Our first algorithm extends the well-known basis pursuit denoising algorithm from the L1 regularizer ∥Ψx∥1 to composite regularizers of the form ∑ d λ d ∥Ψ d x∥1 while self-adjusting the regularization weights λ d . Our second algorithm extends the well-known iteratively reweighted L1 algorithm to the same family of composite regularizers. For each algorithm, we provide several interpretations: i) majorization-minimization (MM) applied to a non-convex log-sum-type penalty, ii) MM applied to an approximate l0-type penalty, iii) MM applied to Bayesian MAP inference under a particular hierarchical prior, and iv) variational expectation-maximization (VEM) under a particular prior with deterministic unknown parameters.A detailed numerical study suggests that, when compared to their non-composite counterparts, our composite algorithms yield significantly improvements in accuracy with only modest increases in computational complexity." @default.
- W2792925054 created "2018-03-29" @default.
- W2792925054 creator A5045693581 @default.
- W2792925054 creator A5046840331 @default.
- W2792925054 date "2017-01-01" @default.
- W2792925054 modified "2023-10-18" @default.
- W2792925054 title "Recovering Signals with Unknown Sparsity in Multiple Dictionaries" @default.
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- W2792925054 doi "https://doi.org/10.1007/978-3-319-69802-1_5" @default.
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