PSWT Based Linear Predictive Coding and Development of a Parallel Multiple Subsequence Structure for DWT Computation

During 1990's the Wavelet Transform emerged as an important signal processing tool with potential applications in time-frequency analysis and non-stationary signal processing.Wavelets have gained popularity in broad range of disciplines like signal/image compression, medical diagnostics, boundary value problems, geophysical signal processing, statistical signal processing,pattern recognition,underwater acoustics etc.In 1993, G. Evangelista introduced the Pitch- synchronous Wavelet Transform, which is particularly suited for pseudo-periodic signal processing.The work presented in this thesis mainly concentrates on two interrelated topics in signal processing,viz. the Wavelet Transform based signal compression and the computation of Discrete Wavelet Transform. A new compression scheme is described in which the Pitch-Synchronous Wavelet Transform technique is combined with the popular linear Predictive Coding method for pseudo-periodic signal processing. Subsequently,A novel Parallel Multiple Subsequence structure is presented for the efficient computation of Wavelet Transform. Case studies also presented to highlight the potential applications.

Classification of Mammograms and DW T based Detection of Microcalcification

Cancer treatment is most effective when it is detected early and the progress in treatment will be closely related to the ability to reduce the proportion of misses in the cancer detection task. The effectiveness of algorithms for detecting cancers can be greatly increased if these algorithms work synergistically with those for characterizing normal mammograms. This research work combines computerized image analysis techniques and neural networks to separate out some fraction of the normal mammograms with extremely high reliability, based on normal tissue identification and removal. The presence of clustered microcalcifications is one of the most important and sometimes the only sign of cancer on a mammogram. 60% to 70% of non-palpable breast carcinoma demonstrates microcalcifications on mammograms [44], [45], [46].WT based techniques are applied on the remaining mammograms, those are obviously abnormal, to detect possible microcalcifications. The goal of this work is to improve the detection performance and throughput of screening-mammography, thus providing a ‘second opinion ‘ to the radiologists. The state-of- the- art DWT computation algorithms are not suitable for practical applications with memory and delay constraints, as it is not a block transfonn. Hence in this work, the development of a Block DWT (BDWT) computational structure having low processing memory requirement has also been taken up.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Generation of self-similar Gaussian time series by means of the DWT and DWPT variance maps

Due to the several kinds of services that use the Internet and data networks infra-structures, the present networks are characterized by the diversity of types of traffic that have statistical properties as complex temporal correlation and non-gaussian distribution. The networks complex temporal correlation may be characterized by the Short Range Dependence (SRD) and the Long Range Dependence - (LRD). Models as the fGN (Fractional Gaussian Noise) may capture the LRD but not the SRD. This work presents two methods for traffic generation that synthesize approximate realizations of the self-similar fGN with SRD random process. The first one employs the IDWT (Inverse Discrete Wavelet Transform) and the second the IDWPT (Inverse Discrete Wavelet Packet Transform). It has been developed the variance map concept that allows to associate the LRD and SRD behaviors directly to the wavelet transform coefficients. The developed methods are extremely flexible and allow the generation of Gaussian time series with complex statistical behaviors.

Fault-tolerant quantum computation with cluster states

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.

A scheme for efficient quantum computation wtih linear optics

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Computation of bifurcation boundaries for power systems: A new Delta-plane method

This paper is devoted to the problems of finding the load flow feasibility, saddle node, and Hopf bifurcation boundaries in the space of power system parameters. The first part contains a review of the existing relevant approaches including not-so-well-known contributions from Russia. The second part presents a new robust method for finding the power system load flow feasibility boundary on the plane defined by any three vectors of dependent variables (nodal voltages), called the Delta plane. The method exploits some quadratic and linear properties of the load now equations and state matrices written in rectangular coordinates. An advantage of the method is that it does not require an iterative solution of nonlinear equations (except the eigenvalue problem). In addition to benefits for visualization, the method is a useful tool for topological studies of power system multiple solution structures and stability domains. Although the power system application is developed, the method can be equally efficient for any quadratic algebraic problem.

A new algorithm and refined bounds for extended gcd computation

Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides refined bounds on the size of the multipliers obtained.

Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. (C) 1997 by John Wiley & Sons, Ltd.

Rapid computation of static fields produced by thick circular solenoids

A straightforward method is proposed for computing the magnetic field produced by a circular coil that contains a large number of turns wound onto a solenoid of rectangular cross section. The coil is thus approximated by a circular ring containing a continuous constant current density, which is very close to the real situation when sire of rectangular cross section is used. All that is required is to evaluate two functions, which are defined as integrals of periodic quantities; this is done accurately and efficiently using trapezoidal-rule quadrature. The solution can be obtained so rapidly that this procedure is ideally suited for use in stochastic optimization, An example is given, in which this approach is combined with a simulated annealing routine to optimize shielded profile coils for NMR.

A flexible method for rapid force computation in elliptical magnets

The design of open-access elliptical cross-section magnet systems has recently come under consideration. Obtaining values for the forces generated within these unusual magnets is important to progress the designs towards feasible instruments. This paper presents a novel and flexible method for the rapid computation of forces within elliptical magnets. The method is demonstrated by the analysis of a clinical magnetic resonance imaging magnet of elliptical cross-section and open design. The analysis reveals the non-symmetric nature of the generated Maxwell forces, which are an important consideration, particularly in the design of superconducting systems.

Read-only-memory-based quantum computation: Experimental explorations using nuclear magnetic resonance and future prospects

Read-only-memory-based (ROM-based) quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less magical, and being more suited to implementing space-efficient computation (i.e., computation using the minimum number of writable qubits). Here we consider a number of small (one- and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using nuclear magnetic resonance ensemble QC. The average fidelities for the implementation were in the ranges 0.9-0.97 for the one-qubit algorithms, and 0.84-0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature real-world problem relating to the lengths of paths in a network.