Optimum Design of Linear Phase Paraunitary Filter Bank & its Applications in Signal Processing

Filter Banks plays crucial role in signal processing and image processing as subband processing gives dominant results in time critical applications. In formal years, various Para unitary Linear Phase Filter Banks are proposed by following conventional and computational complex factorization and lattice approaches consisting of complex nonlinear optimization problems. One of the recent methods to design Filter Bank having properties of Linear Phase and Paraunitary is via Singular value decomposition technique which leads to optimum results compared to existing methods as most of the time it deals with matrix operations. In this paper, design benchmark is evaluated as two dominant optimization queries and reasonable key of each optimization query is solved by performing Singular Value Decomposition. Proposed Paper discusses linear phase condition of filter banks satisfying mirror image symmetry at analysis side and perfect reconstruction property at synthesis side. Singular Value Decomposition approach leads to fast and efficient simulation results compared to existing filter banks designs. Proposed method of filter bank design deals with any arbitrary channels and every length of the filters

On the design of two-channel 2-D nonseparable multi-plet perfect reconstruction filter banks

This paper proposes a new design method for a class of two-channel 2D non-separable perfect reconstruction (PR) filter banks (FBs) using the multiplet FBs. 1D multiplet FBs are PR FBs that can be obtained by frequency transformation of a prototype PR FB in the conventional lifting structure so that a better frequency characteristics can be obtained and varied online to process different signals. By employing the 1D to 2D transformation of Phoong et al., new 2D PR multiplet FBs with quincunx, hourglass, and parallelogram spectral support are obtained. These nonseparable multiplet FBs can be cascaded to realize new PR directional FB for image processing and motion analysis. The design procedure is very general and it can be applied to both linear-phase and low-delay 2D FBs. Design examples are given to demonstrate the usefulness of the proposed method.published_or_final_versio

Sampling from a system-theoretic viewpoint

This paper studies a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. \ud \ud The paper is split into three parts. In Part I we present the paradigm and revise the lifting technique, which is our main technical tool. In Part II optimal samplers and holds are designed for various analog signal reconstruction problems. In some cases one component is fixed while the remaining are designed, in other cases all three components are designed simultaneously. No causality requirements are imposed in Part II, which allows to use frequency domain arguments, in particular the lifted frequency response as introduced in Part I. In Part III the main emphasis is placed on a systematic incorporation of causality constraints into the optimal design of reconstructors. We consider reconstruction problems, in which the sampling (acquisition) device is given and the performance is measured by the $L^2$-norm of the reconstruction error. The problem is solved under the constraint that the optimal reconstructor is $l$-causal for a given $l\geq 0,$ i.e., that its impulse response is zero in the time interval $(-\infty,-l h),$ where $h$ is the sampling period. We derive a closed-form state-space solution of the problem, which is based on the spectral factorization of a rational transfer function

Image coding for digitized libraries

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1998.Thesis (Ph.D.) -- Bilkent University, 1998.Includes bibliographical references leaves 104-113III this thesis, image coding methods for two basic image types are developed under a digitized library framework. The two image types are gray tone or color images, and binary textual images, which are the digitized image versions of text documents. The grciy tone images are encoded using an adaptive subband decomposition followed by zerotree quantizers. The adaptive sub- l)and decomposition filter bank adaptively updates the filter bank coefficients in which the values of one of the subbands is predicted from the other sub- band. It is observed that the adaptive subband decomposition performs better than a regulcir subband decomposition with a fixed filter bank in terms of compression. For the binary textual images, a compression algorithm using binary subband decomposition followed by a textual image compression (TIC) method that exploits the redundancy in repeating characters is developed. The binary subband decomposition yields binary sub-images, and the TIC method is applied to the low band sub-image. Obtaining binary sub-images improves compression results as well as pattern matching time of the TIC method. Simulation results for both adaptive subband decomposition and multiresolution TIC methods indicate improvements over the methods described in the literature.Gerek, Ömer NezihPh.D

Development Of Efficient Multi-Level Discrete Wavelet Transform Hardware Architecture For Image Compression

Berfokuskan pengkomputeran intensif dalam gelombang kecil diskret (DWT), reka bentuk seni bina perkakasan efisen bagi pengkomputeran laju menjadi imperatif terutamanya dalam aplikasi masa nyata. Focusing on the intensive computations involved in the discrete wavelet transform (DWT), the design of efficient hardware architectures for a fast computation of the transform has become imperative, especially for real-time applications

Image restoration: Wavelet frame shrinkage, nonlinear evolution PDEs, and beyond

In the past few decades, mathematics based approaches have been widely adopted in various image restoration problems; the partial differential equation (PDE) based approach (e.g., the total variation model [L. Rudin, S. Osher, and E. Fatemi, Phys. D, 60 (1992), pp. 259-268] and its generalizations, nonlinear diffusions [P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intel., 12 (1990), pp. 629-639; F. Catte et al., SIAM J. Numer. Anal., 29 (1992), pp. 182-193], etc.) and wavelet frame based approach are some successful examples. These approaches were developed through different paths and generally provided understanding from different angles of the same problem. As shown in numerical simulations, implementations of the wavelet frame based approach and the PDE based approach quite often end up solving a similar numerical problem with similar numerical behaviors, even though different approaches have advantages in different applications. Since wavelet frame based and PDE based approaches have all been modeling the same types of problems with success, it is natural to ask whether the wavelet frame based approach is fundamentally connected with the PDE based approach when we trace them all the way back to their roots. A fundamental connection of a wavelet frame based approach with a total variation model and its generalizations was established in [J. Cai, B. Dong, S. Osher, and Z. Shen, J. Amer. Math. Soc., 25 (2012), pp. 1033-1089]. This connection gives the wavelet frame based approach a geometric explanation and, at the same time, it equips a PDE based approach with a time frequency analysis. Cai et al. showed that a special type of wavelet frame model using generic wavelet frame systems can be regarded as an approximation of a generic variational model (with the total variation model as a special case) in the discrete setting. A systematic convergence analysis, as the resolution of the image goes to infinity, which is the key step in linking the two approaches, is also given in Cai et al. Motivated by Cai et al. and [Q. Jiang, Appl. Numer. Math., 62 (2012), pp. 51-66], this paper establishes a fundamental connection between the wavelet frame based approach and nonlinear evolution PDEs, provides interpretations and analytical studies of such connections, and proposes new algorithms for image restoration based on the new understandings. Together with the results in [J. Cai et al., J. Amer. Math. Soc., 25 (2012), pp. 1033-1089], we now have a better picture of how the wavelet frame based approach can be used to interpret the general PDE based approach (e.g., the variational models or nonlinear evolution PDEs) and can be used as a new and useful tool in numerical analysis to discretize and solve various variational and PDE models. To be more precise, we shall establish the following: (1) The connections between wavelet frame shrinkage and nonlinear evolution PDEs provide new and inspiring interpretations of both approaches that enable us to derive new PDE models and (better) wavelet frame shrinkage algorithms for image restoration. (2) A generic nonlinear evolution PDE (of parabolic or hyperbolic type) can be approximated by wavelet frame shrinkage with properly chosen wavelet frame systems and carefully designed shrinkage functions. (3) The main idea of this work is beyond the scope of image restoration. Our analysis and discussions indicate that wavelet frame shrinkage is a new way of solving PDEs in general, which will provide a new insight that will enrich the existing theory and applications of numerical PDEs, as well as those of wavelet frames