An affine scaling methodology for best basis selection

By Bhaskar D. Rao, Kenneth Kreutz-Delgado. 1999

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Citations in the corpus

Multimodal Multipart Learning for Action Recognition in Depth Videos (2015, methodology): “To apply the modality based coupling over heterogeneous features of each part, it applies a mixed norm with two degrees of “diversity” induction [4], fol-”
Sparse Coding via Thresholding and Local Competition in Neural Circuits (2008, methodology): “While FOCUSS can implement both ℓ 1 global optimization and ℓ 0 local optimization (Rao and Kreutz-Delgado, 1999) in a dynamical system (Kreutz-Delgado et al., 2003) that uses parallel computation to implement a competition strategy among the nodes (strong nodes are encouraged to grow while weak nod”
An efficient algorithm for compressed MR imaging using total variation and wavelets (2008, methodology): “Minimizing an p-quasinorm for 0 ≤ p < 1 may achieve a higher compression ratio [6, 7] than p = 1 but since the objective function is nonconvex, the p-algorithms, including FOCUSS [22] and the recent ones by Candès et al.”
K-SVD and its non-negative variant for dictionary design (2005, methodology): “The Focal Under-determined System Solver (FOCUSS) is very similar, using the `-norm with p ≤ 1, as a replacement to the `norm [5].”
Iterative Reweighted 1 and 2 Methods for Finding Sparse Solutions (2010, methodology): “The FOCUSS algorithm [20] can also be viewed as an iterative reweighted 2 method for locally solving (13) for the special case when = 0; however, Candès et al. point out that just a few iterations of their method is far more effective in finding sparse solutions than FOCUSS.”
Iteratively reweighted algorithms for compressive sensing (2008, methodology): “The case of p < 1 was studied by Rao and Kreutz-Delgado [2].”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, methodology): “A simple strategy to attack (Q1 ) is the iteratively reweighted least squares (IRLS) algorithm [97, 139, 138].”
Comparing Measures of Sparsity (2008, background): “For measuring ‘diversity’, [37], [38] use some different measures.”
Sparse Bayesian learning for basis selection (2004, methodology): “In fact, it can be shown that finding this MAP estimate is equivalent to finding the minimum -norm solution using FOCUSS with [3].”
Sparse Methods for Direction-of-Arrival Estimation (2016, methodology): “A regularized FOCUSS algorithm for (27) was developed in [30] by using the same main idea as in FOCUSS.”
Theoretical Results on Sparse Representations of Multiple-Measurement Vectors (2006, background): “In the pioneer works on MMV [1], [20], [21], the following diversity measure on sparsity was proposed:”
Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data (2009, background): “Also, the success of total-variation regularization for image restoration indicates that most images can be well approximated by those having a sparse gradient.”
Sparse regression using mixed norms (2009, methodology): “In the problem we consider, point iii) does not matter, becauseA is here a continuous function. Point i) can be proved exactly as in [ 24 ].”
$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation (2006, methodology): “The Focal Under-determined System Solver (FOCUSS) is very similar, using the "p-norm with p ≤ 1, as a replacement to the "0-norm [18], [19], [20], [21].”
Exact Reconstruction of Sparse Signals via Nonconvex Minimization (2007, methodology): “More sophisticated algorithms are possible; for example , the FOCUSS approach of Rao and Kreutz-Delgado [10] (though this would not be feasible for the examples of the next section, where a gradient operator needs to be incorporated).”
A sparse signal reconstruction perspective for source localization with sensor arrays (2005, background): “The discussion in [15] in Section VI indicates that the best results are obtained for close to 1, whereas the convergence is also slowest for .”