Phase local approximation (PhaseLa) technique for phase unwrap from noisy data.

The local polynomial approximation (LPA) is a nonparametric regression technique with pointwise estimation in a sliding window. We apply the LPA of the argument of cos and sin in order to estimate the absolute phase from noisy wrapped phase data. Using the intersection of confidence interval (HCI) algorithm, the window size is selected as adaptive pointwise varying. This adaptation gives the phase estimate with the accuracy close to optimal in the mean squared sense. For calculations, we use a Gauss-Newton recursive procedure initiated by the phase estimates obtained for the neighboring points. It enables tracking properties of the algorithm and its ability to go beyond the principal interval [-pi, pi] and to reconstruct the absolute phase from wrapped phase observations even when the magnitude of the phase difference takes quite large values. The algorithm demonstrates a very good accuracy of the phase reconstruction which on many occasion overcomes the accuracy of the state-of-the-art algorithms developed for noisy phase unwrap. The theoretical analysis produced for the accuracy of the pointwise estimates is used for justification of the HCI adaptation algorithm.     

Complexity of the consistency problem for certain Post classes

The complexity of the consistency problem for several important classes of Boolean functions is analyzed. The classes of functions under investigation are those which are closed under function composition or superposition. Several of these so-called Post classes are considered within the context of machine learning with an application to breast cancer diagnosis. The considered Post classes furnish a user-selectable measure of reliability. It is shown that for realistic situations which may arise in practice, the consistency problem for these classes of functions is polynomial-time solvable.     

Tree-Structured Haar Transforms

The Haar transform is generalized to the case of an arbitrary time and scale splitting. To any binary tree we associate an orthogonal system of Haar-type functions – tree-structured Haar (TSH) functions. Unified fast algorithm for computation of the introduced tree-structured Haar transforms is presented. It requires 2(N – 1) additions and 3N –2 multiplications, where N is transform order or, equivalently, the number of leaves of the binary tree.     

Asymptotic behavior of morphological filters

The connection between morphological and stack filters is used in the analysis of the statistical properties of morphological filters. Closed-form expressions for the output distributions of morphological filters are given, and their statistical symmetry properties are analyzed. Asytotically tight bounds on the expectations of two-dimensional morphological filters, and asymptotic formulas for the variances of one-dimensional morphological filters are derived. These results form the basis for analyzing general asymptotic properties of morphological filters.     

Fibonacci Arithmetic Expressions

In this paper, we extend the arithmetic (AR) expressions for functions on finite dyadic groups to functions used in Fibonacci interconnection topologies. We have introduced the Fibonacci-Arithmetic (FibAR) expressions for representation of these functions. We discussed the optimization of FibARs with respect to the number of non-zero coefficients through the Fixed-Polarity FibARs defined by using different polarities for the Fibonacci variables. In this way, we provide a base to extend the application of ARs and related powerful CAD design tools for switching functions to functions in Fibonacci interconnection topologies.     

A New Tensorial Framework for Single-Shell High Angular Resolution Diffusion Imaging

Single-shell high angular resolution diffusion imaging data (HARDI) may be decomposed into a sum of eigenpolynomials of the Laplace-Beltrami operator on the unit sphere. The resulting representation combines the strengths hitherto offered by higher order tensor decomposition in a tensorial framework and spherical harmonic expansion in an analytical framework, but removes some of the conceptual weaknesses of either. In particular it admits analytically closed form expressions for Tikhonov regularization schemes and estimation of an orientation distribution function via the Funk-Radon Transform in tensorial form, which previously required recourse to spherical harmonic decomposition. As such it provides a natural point of departure for a Riemann-Finsler extension of the geometric approach towards tractography and connectivity analysis as has been stipulated in the context of diffusion tensor imaging (DTI), while at the same time retaining the natural coarse-to-fine hierarchy intrinsic to spherical harmonic decomposition.     

Vector median filters

Two nonlinear algorithms for processing vector-valued signals are introduced. The algorithms, called vector median operations, are derived from two multidimensional probability density functions using the maximum-likelihood-estimate approach. The underlying probability densities are exponential, and the resulting operations have properties very similar to those of the median filter. In the vector median approach, the samples of the vector-valued input signal are processed as vectors. The operation inherently utilizes the correlation between the signal components, giving the filters some desirable properties. General properties as well as the root signals of the vector median filters are studied. The vector median operation is combined with linear filtering, resulting in filters with improved noise attenuation and filters with very good edge response. An efficient algorithm for implementing long vector median filters is presented. The noise attenuation of the filters is discussed, and an application to velocity filtering is shown     

DNA sequence compression - Based on the normalized maximum likelihood model

Genomic data provide challenging problems that have been studied in a number of fields such as statistics, signal processing, information theory, and computer science. This article shows that the methodologies and tools that have been recently developed in these fields for modeling signals and processes appear to be most promising for genomic research     

Robust Index Assignment Using Hadamard Transform for Vector Quantization Transmission over Finite-Memory Contagion Channels

This paper presents a new index assignment (IA) method when vector quantization indices are transmitted over a particular class of Markov binary channels, namely the finite-memory contagion channels. (See F. Alajaji and T. Fuja, IEEE Trans. Inform. Theory, 40:2035-2041, 1994.) For this class of binary channels, the Hadamard transform of the vector formed with noise pattern probabilities obeys well-structured recursions, allowing an efficient evaluation of the channel distortion and also revealing a useful approximation based on the dominant terms in the channel distortion expression. The proposed IA method minimizes the distortion approximation and is very robust to changes in the parameters of the channel model. The same technique applies for both maximum likelihood and mean-squared error decoding methods. The IA algorithm is applied to the transmission of line spectral frequency parameters quantized as in the G.729 standard to show the usefulness of the proposed method.