Linear Programming Algorithms for Sparse Filter Design

Baran, Thomas A.; Wei, Dennis; Oppenheim, Alan V.

doi:10.1109/tsp.2009.2036471

Cited by 117 publications

(90 citation statements)

References 32 publications

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“…This means that the size of the optimization problem solved shrinks at each iteration, speeding up the running time of the overall algorithm. If the change in the solution x is below stop from one iteration to the next, as checked in (12), then the procedure is terminated because further iterations will not make any progress. In the case of the 2D filters, we have modified the usual reweighting rule in (13) because there exists an extra incentive to nullify coefficients that belong to theH 33 matrix: these coefficients participate four times in the final matrix H, as opposed to only two times for the others (and once for the central coefficient).…”

Section: Design Of Sparse Filtersmentioning

confidence: 99%

“…The idea is to try to further eliminate the coefficients of the solutions that are the smallest in absolute value while keeping the optimization problem (15) feasible. This stage applies exactly the smallest coefficient rule (SCR) presented in [12].…”

Section: Design Of Sparse Filtersmentioning

confidence: 99%

“…The two most popular approaches that are used to induce sparsity are: convex relaxation to l 1 minimization [9] and greedy methods [10]. In this sense, previous work for sparse filter design includes the use of the orthogonal matching pursuit algorithm [11], greedy coefficient elimination [12] and linear programming [12], [13], [14]. In this paper we consider a combination of the two approaches to design filters in the minimax sense.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Iterative reweighted l1 design of sparse FIR filters

Rusu

Dumitrescu

2012

Signal Processing

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Designing sparse 1D and 2D filters has been the object of research in recent years due mainly to the developments in the field of sparse representations. The main goal is to reduce the implementation complexity of a filter while keeping as much of the performance as possible. This paper describes a new method for designing sparse filters in the minimax sense using a mixture of reweighted l 1 minimization and greedy iterations. The combination proves to be quite efficient; after the reweighted l 1 minimization stage is used to introduce zero coefficients in bulk, a small number of greedy iterations serve to eliminate a few extra coefficients. Experimental results and a comparison with the latest methods show that the proposed method performs very well both in the running speed and in the quality of the solutions obtained.

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Section: Design Of Sparse Filtersmentioning

confidence: 99%

Section: Design Of Sparse Filtersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Iterative reweighted l1 design of sparse FIR filters

Rusu

Dumitrescu

2012

Signal Processing

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“…The development of design techniques for sparse FIR filters has been active in the past several years in the signal processing society, see, e.g., Baran et al (2010), Lu and Hinamoto (2011), Rusu and Dumitrescu (2012). However it was mainly limited to single 1D and 2D filters.…”

Section: Introductionmentioning

confidence: 99%

Sparsity optimization in design of multidimensional filter networks

et al. 2015

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Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality. They are composed of sparse sub-filters whose high sparsity ensures fast image processing. The filter network design is related to solving a sparse optimization problem where a cardinality constraint bounds above the sparsity level. In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinalityconstrained multilinear least-squares (MLLS) problem is to be solved.Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated. The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented. It is then applied to solving a bi-criteria optimization problem in which both the time and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

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“…This algorithm is shown to provide efficient allocations at a relatively low computational cost. There has been various greedy algorithms as well as convex relaxation based approach to sparse filter design in the literature [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Sparse approximation based resource allocation in DSL/DMT transceivers with per-tone equalization

2014

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a b s t r a c tPer-tone equalization has been proposed as an alternative to time domain equalization for DMT receivers in DSL modems. It optimizes the bit rate performance of the receiver as each tone can be equalized independently. It has also been shown that using variable length equalizers can significantly reduce the total number of equalizer taps and hence the run-time complexity, without compromising performance. For a given transmit power loading, it has been shown that the equalizer taps can be allocated optimally using a dual decomposition based approach with per-tone exhaustive searches over all possible equalizer lengths. However, a more general approach is needed when optimal transmit power allocation is also considered to maximize the overall bit rate, where in addition the per-tone exhaustive searches are replaced by a more efficient procedure. In this paper, a sparse approximation based resource allocation algorithm is presented to allocate equalizer taps and transmit power over tones and maximize the overall bit rate. This algorithm is shown to provide efficient allocations at a relatively low computational cost.

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Linear Programming Algorithms for Sparse Filter Design

Cited by 117 publications

References 32 publications

Iterative reweighted l1 design of sparse FIR filters

Iterative reweighted l1 design of sparse FIR filters

Sparsity optimization in design of multidimensional filter networks

Sparse approximation based resource allocation in DSL/DMT transceivers with per-tone equalization

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