Design of synthesis filter banks for the structural similarity index

Chai, Lu; Sheng, Yuxia; Zhang, Jingxin

doi:10.1109/icip.2013.6738175

Cited by 4 publications

(6 citation statements)

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“…A preliminary result has been reported for a special class of filter banks with the filter length equal to the decimation number [17]. The proof idea of Theorem 1 in this paper comes from [17]. However, this paper is essentially different to [17].…”

Section: Introductionmentioning

confidence: 93%

“…It is natural to introduce SSIM index into the optimal design of filter banks. A preliminary result has been reported for a special class of filter banks with the filter length equal to the decimation number [17]. The proof idea of Theorem 1 in this paper comes from [17].…”

Section: Introductionmentioning

confidence: 97%

“…The proof idea of Theorem 1 in this paper comes from [17]. However, this paper is essentially different to [17]. The subband signals and the reconstructed signals are wide sense cyclo-stationary in filter bank systems instead of wide sense stationary (WSS) in this paper, due to the rate-changing operation [18], [19].…”

Section: Introductionmentioning

confidence: 99%

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Optimal Design of Multichannel Equalizers for the Structural Similarity Index

Chai

Sheng

2014

IEEE Trans. on Image Process.

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The optimization of multichannel equalizers is studied for the structural similarity (SSIM) criteria. The closed-form formula is provided for the optimal equalizer when the mean of the source is zero. The formula shows that the equalizer with maximal SSIM index is equal to the one with minimal mean square error (MSE) multiplied by a positive real number, which is shown to be equal to the inverse of the achieved SSIM index. The relation of the maximal SSIM index to the minimal MSE is also established for given blurring filters and fixed length equalizers. An algorithm is also presented to compute the suboptimal equalizer for the general sources. Various numerical examples are given to demonstrate the effectiveness of the results.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 97%

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Optimal Design of Multichannel Equalizers for the Structural Similarity Index

Chai

Sheng

2014

IEEE Trans. on Image Process.

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“…Even then the matrix representations developed in this paper for various multirate operations have been successfully applied to deal with it. Continuing forward, we use the above relation in (58) and obtain…”

Section: A Pseudocirculant Propertymentioning

confidence: 99%

“…However, the solution presented was for two channels only. In [58], Li Chai et al formulated the problem using structural similarity criterion and obtained closed-form solution under certain assumptions like the filter length is equal to the decimation factor, the mean of the source is zero, etc. Compresive sensing based method was used in [59] to estimate a signal from multirate observations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Signals via Non-Maximally Decimated Non-Uniform Filter Banks

Patel

Dhuli

Lall

2019

IEEE Trans. Circuits Syst. I

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This paper addresses the important problem of reconstructing a signal from multiple multirate observations. The observations are modeled as the output of an analysis bank, and time-domain analysis is carried out to design an optimal FIR synthesis bank. We pose this as a minimizing the mean-square problem and prove that at least one optimal solution is always possible. A parametric form for all optimal solutions is obtained for a non-maximally decimated filter bank. The necessary and sufficient conditions for an optimal solution, that results in perfect reconstruction (PR), are derived as time-domain pseudocirculant conditions. This represents a novel theoretical contribution in multirate filter bank theory. We explore PR in a more general setting. This results in the ability to design a synthesis bank with a particular delay in the reconstruction. Using this delay, one can achieve PR in cases where it might not have been possible otherwise. Further, we extend the design and analysis to nonuniform filter banks and carry out simulations to verify the derived results.

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