Filtering in Rotated Time-Frequency Domains With Unknown Noise Statistics

Subramaniam, Suba R.; Ling, Bingo Wing‐Kuen; Georgakis, Apostolos

doi:10.1109/tsp.2011.2171956

Cited by 27 publications

(7 citation statements)

References 12 publications

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“…Linear and non‐adaptive time–frequency denoising techniques are found to be useful for suppressing the noise [3]. However, the denoising performances of these conventional linear and non‐adaptive time–frequency denoising techniques such as those based on the discrete fractional Fourier transform [4] and the discrete‐time wavelet transform [5] are highly dependent on the chosen linear kernels. In general, there is no simple rule for choosing these linear kernels.…”

Section: Introductionmentioning

confidence: 99%

Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Lin

Ling

et al. 2018

IET signal process.

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This study proposes an integer quadratic programming method for grouping and selecting the singular spectral analysis components based on the empirical mode decomposition for performing the denoising. Here, the total number of the grouped singular spectral analysis components is equal to the total number of the intrinsic mode functions. The singular spectral analysis components are assigned to the group indexed by the corresponding intrinsic mode function where the two norm error between the corresponding intrinsic mode function and the sum of the grouped singular spectral analysis components is minimum. Actually, this assignment of the singular spectral analysis components to a particular group is an integer quadratic programming problem. However, the required computational power for finding the solution of the integer quadratic programming problem is high. On the other hand, by representing the integer quadratic programming problem as an integer linear programming problem and employing an existing numerical optimisation computer aided design tool for finding the solution of the integer linear programming problem, the solution can be found efficiently. Computer numerical simulation results are presented.

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Section: Introductionmentioning

confidence: 99%

Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Lin

Ling

et al. 2018

IET signal process.

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“…As a result, the performances of all the existing applications based on either the FT or the time-domain linear operations can be improved or maintained if the FT or the time-domain linear operations is replaced by the appropriate FrFT. Owing to this reason, many signal processing applications based on the representations of the signals in the discrete FrFT (DFrFT) domains such as the filtering of signals [2][3][4][5], the sampling and the reconstructions of signals [6][7][8], the watermarking as well as the encryptions and the decryptions of images [9,10], the compressions of magnetic resonance images [11][12][13] have been developed.…”

Section: Introductionmentioning

confidence: 99%

Optimal design of orders of DFrFTs for sparse representations

Zhang

Ling

Tao

et al. 2018

IET signal process.

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This paper proposes an optimal design of the orders of the discrete fractional Fourier transforms (DFrFTs) and construct an overcomplete transform using the DFrFTs with these orders for performing the sparse representations. The design problem is formulated as an optimization problem with an 1 L norm nonconvex objective function. To avoid all the orders of the DFrFTs to be the same, the exclusive OR of two constraints are imposed. The constrained optimization problem is further reformulated to an optimal frequency sampling problem. A method based on solving the roots of a set of harmonic functions is employed for finding the optimal sampling frequencies. As the designed overcomplete transform can exploit the physical meanings of the signals in terms of representing the signals as the sums of the components in the time frequency plane, the designed overcomplete transform can be applied to many applications.

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“…The decision vectors are discrete valued. One common approach to address this issue is to approximate the problems by the optimization problems with continuous valued decision vectors and some advanced techniques [2,3,4,5] are applied to find the solution of these problems. To address the original optimization with the discrete valued decision vectors, the 0-1 multidimensional knapsack problem (MKP) is a well-known NP-hard optimization problem [6].…”

Section: Introductionmentioning

confidence: 99%

Binary artificial algae algorithm for multidimensional knapsack problems

Zhang

et al. 2016

Applied Soft Computing

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The multidimensional knapsack problem (MKP) is a well-known NP-hard optimization problem. Various meta-heuristic methods are dedicated to solve this problem in literature. Recently a new meta-heuristic algorithm, called artificial algae algorithm (AAA), was presented, which has been successfully applied to solve various continuous optimization problems. However, due to its continuous nature, AAA cannot settle the discrete problem straightforwardly such as MKP. In view of this, this paper proposes a binary artificial algae algorithm (BAAA) to efficiently solve MKP. This algorithm is composed of discrete process, repair operators and elite local search. In discrete process, two logistic functions with different coefficients of curve are studied to achieve good discrete process results. Repair operators are performed to make the solution feasible and increase the efficiency. Finally, elite local search is introduced to improve the quality of solutions. To demonstrate the efficiency of our proposed algorithm, simulations and evaluations are carried out with total of 94 benchmark problems and compared with other bio-inspired state-of-the-art algorithms in the recent years including MBPSO, BPSOTVAC, CBPSOTVAC, GADS, bAFSA, and IbAFSA. The results show the superiority of BAAA to many compared existing algorithms.

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Filtering in Rotated Time-Frequency Domains With Unknown Noise Statistics

Cited by 27 publications

References 12 publications

Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Grouping and selecting singular spectral analysis components for denoising based on empirical mode decomposition via integer quadratic programming

Optimal design of orders of DFrFTs for sparse representations

Binary artificial algae algorithm for multidimensional knapsack problems

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