Optimal Design Of Synthesis Filter Banks For Image Processing

Filter banks have been widely applied to many engineering fields as imageprocessing, coding theory, digital communication and robust information transmission.In these applications it is of great importance to design the optimal synthesis filter bankfor different criteria. This dissertation deals with the optimal design of synthesis filterbanks with optimal MSE and SSIM index, which are two typical image qualityassessment indexes. Specifically, we present effective methods to design the optimalsynthesis filter bank with lattice structure constraints and post-filter in lapped transformfor MSE measurement. The problem of designing the equalizer with optimal SSIMindex has also been solved. The main contributions are as follows:1) Methods of designing optimal synthesis filter banks with lattice structure areproposed. For the subband noise with known power spectral density (PSD), the explicitformulae are derived using the Lyapunov equation. For the subband noise withunknown PSD, the convex optimization algorithm is presented to minimize theworst-case reconstruction error. The design method of linear phase separable twodimensional synthesis filter banks is studied. For a given linear phase oversampled filterbank applied to row and column processing, the optimal linear phase synthesis filterbanks are designed for row and column processing respectively. The effectiveness ofthese solutions is demonstrated by numerical examples.2) The optimal post-filter for time domain oversampled lapped transform (TDOLT)is presented. The explicit formulae of post-filters are given for TDOLT and partialTDOLT for noise with known PSD by minimizing the power norm of reconstructionerror. For the subband noise with unknown PSD, a worst-case design algorithm isdeveloped to compute the post-filter by solving linear matrix inequalities. Moreover, amethod is proposed for the multistage TDOLT. The obtained optimal post-filters areapplied to JPEG codec. The performance of improving coding efficiency and reducingblocking are demonstrated by examples. 3) The problem of designing the equalizer with optimal SSIM index is solved forgeneral multichannel systems. The closed form formula is provided for the equalizerwith maximal SSIM index when the mean of the source is zero. One interesting andimportant result is that the equalizer with maximal SSIM index is equal to the one withminimal MSE multiplied by a positive real number, which is shown to be equal to theinverse of the achieved SSIM index. The relation between the maximal SSIM index andthe minimal MSE has been established for fixed blurring filters and the length ofequalizers. An algorithm is presented to compute the suboptimal equalizer for thegeneral sources of which the mean is not zero. Various simulations have been given todemonstrate the effectiveness of the results.4) A method to design the post-filter based on SSIM index for lapped transform isproposed. Under the assumption that the source signal is a wide sense stationary processwith known PSD, that the noise is Gaussian white, and that the filter length is equal tothe decimation number, the closed-form solution is obtained. The method is applied inthe reconstruction of DCT coding systems. Experimental results show that comparedwith IDCT and MSE based method, the proposed method can achieve better structurefeature while maintaining satisfactory ability of noise reduction.