Optimal Design of Multichannel Equalizers for the Structural Similarity Index

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.

[1]  L. Tong,et al.  Multichannel blind identification: from subspace to maximum likelihood methods , 1998, Proc. IEEE.

[2]  Edoardo Mosca,et al.  Optimal Noise Reduction in Oversampled PR Filter Banks , 2009, IEEE Transactions on Signal Processing.

[3]  Karim Abed-Meraim,et al.  Blind system identification , 1997, Proc. IEEE.

[4]  Edward R. Vrscay,et al.  SSIM-inspired image restoration using sparse representation , 2012, EURASIP Journal on Advances in Signal Processing.

[5]  Jingxin Zhang,et al.  Design of synthesis filter banks for the structural similarity index , 2013, 2013 IEEE International Conference on Image Processing.

[6]  Nikolas P. Galatsanos,et al.  Least squares restoration of multichannel images , 1991, IEEE Trans. Signal Process..

[7]  Alan C. Bovik,et al.  Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures , 2009, IEEE Signal Processing Magazine.

[8]  Robert W. Heath,et al.  A Linear Estimator Optimized for the Structural Similarity Index and its Application to Image Denoising , 2006, 2006 International Conference on Image Processing.

[9]  Li Qiu,et al.  Fundamental performance limitations in estimation problems , 2002, Commun. Inf. Syst..

[10]  Jingxin Zhang,et al.  Robust optimal post-filter in oversampled lapped transform: Theory and application in image coding , 2013, Signal Process..

[11]  Robert W. Heath,et al.  SSIM-optimal linear image restoration , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[12]  Wen Gao,et al.  Rate-SSIM optimization for video coding , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[13]  Thomas Richter,et al.  A MS-SSIM Optimal JPEG 2000 Encoder , 2009, 2009 Data Compression Conference.

[14]  Fabrice Labeau.  Synthesis filters design for coding gain in oversampled filter banks , 2005, IEEE Signal Processing Letters.

[15]  Homer H. Chen,et al.  Perceptual Rate-Distortion Optimization Using Structural Similarity Index as Quality Metric , 2010, IEEE Transactions on Circuits and Systems for Video Technology.

[16]  Hans Burkhardt,et al.  Multichannel image restoration based on optimization of the structural similarity index , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[17]  Wilhelm Burger,et al.  Digital Image Processing - An Algorithmic Introduction using Java , 2008, Texts in Computer Science.

[18]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[19]  Jan Flusser,et al.  A Unified Approach to Superresolution and Multichannel Blind Deconvolution , 2007, IEEE Transactions on Image Processing.

[20]  Zhou Wang,et al.  On the Mathematical Properties of the Structural Similarity Index , 2012, IEEE Transactions on Image Processing.

[21]  Robert W. Heath,et al.  Design of Linear Equalizers Optimized for the Structural Similarity Index , 2008, IEEE Transactions on Image Processing.

[22]  Philippe Loubaton,et al.  A subspace algorithm for certain blind identification problems , 1997, IEEE Trans. Inf. Theory.

[23]  K. Siddaraju,et al.  DIGITAL IMAGE RESTORATION , 2011 .

[24]  Jingxin Zhang,et al.  Optimal Design of Oversampled Synthesis FBs With Lattice Structure Constraints , 2011, IEEE Transactions on Signal Processing.

[25]  Holger Boche,et al.  Structural Properties of the Wiener Filter—Stability, Smoothness Properties, and FIR Approximation Behavior , 2006, IEEE Transactions on Information Theory.

[26]  Richard G. Baraniuk,et al.  ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems , 2004, IEEE Transactions on Signal Processing.

[27]  Jan Flusser,et al.  Multichannel blind deconvolution of spatially misaligned images , 2005, IEEE Transactions on Image Processing.

[28]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[29]  Edward R. Vrscay,et al.  SSIM-inspired image denoising using sparse representations , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[30]  Biao Huang,et al.  On spectral theory of cyclostationary signals in multirate systems , 2005, IEEE Trans. Signal Process..

[31]  Eero P. Simoncelli,et al.  Image restoration using Gaussian scale mixtures in the wavelet domain , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[32]  T. Aach.  Comparative Analysis of Shift Variance and Cyclostationarity in Multirate Filter Banks , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  Peter Maurer,et al.  Algorithms For Statistical Signal Processing , 2016 .

[34]  Lai-Man Po,et al.  An SSIM-optimal H.264/AVC inter frame encoder , 2009, 2009 IEEE International Conference on Intelligent Computing and Intelligent Systems.

[35]  Robert W. Heath,et al.  Rate Bounds on SSIM Index of Quantized Images , 2008, IEEE Transactions on Image Processing.