Blind deconvolution of symmetric noncausal impulse responses usingtwo-sided linear prediction

Considers the problem of estimating the time-symmetric, noncausal impulse response of a linear time-invariant system from measurements of the response of the system to an unknown input signal, which is assumed to be a realization of a white random process. The symmetric impulse response is modeled by a two-sided AR or ARMA system model. The two-sided AR coefficients are estimated using a two-step procedure. First, an estimate of an unconstrained parameter vector is computed by solving a close-to-Toeplitz-plus-Hankel system of equations using previously developed fast algorithms. Then, the polynomial square root of the result is obtained by solving a constrained least-squares problem which has a simple solution. Unlike previous methods, this approach requires no iterative procedure. However, it may lead to an unstable model in some extreme cases. Simulation results illustrate the performance of the proposed methods     

Discrete fast algorithms for two-dimensional linear prediction on apolar raster

New generalized split Levinson and Schur algorithms for the two-dimensional linear least squares prediction problem on a polar raster are derived. The algorithms compute the prediction filter for estimating a random field at the edge of a disk from noisy observations inside the disk. The covariance function of the random field is assumed to have a Toeplitz-plus-Hankel structure for both its radial part and its transverse (angular) part. This assumption is valid for some types of random fields, such as isotropic random fields. The algorithms generalize the split Levinson and Schur algorithms in two ways: (1) to two dimensions; and (2) to Toeplitz-plus-Hankel covariances     

Equations for the angles of arrival and departure for multivariable root loci using frequency-domain methods

Frequency-domain methods are used to study the angles of arrival and departure for multivariable root loci. Explicit equations are obtained. For a special class of poles and zeros, some simpler equations that are generalizations of the single-input-single-output equations are presented.     

The gradient adaptive split lattice algorithm

The authors present a new algorithm for adaptive filtering of autoregressive processes, based on a three-term recurrence that replaces the lattice equations of the gradient adaptive lattice (GAL) algorithm of Griffiths (1977) and requires only half as many multiplications per recursion. They also present a single-stage convergence analysis and a numerical example comparing the new algorithm to the GAL. Its performance is similar to the GAL, while requiring less than 2/3 as many multiplications and additions     

Region-of-interest tomography using exponential radial sampling

The authors combine several ideas, including nonuniform sampling and circular harmonic expansions, into a new procedure for reconstructing a small region of interest (ROI) of an image from a set of its projections that are densely sampled in the ROI and coarsely sampled outside the ROI. Specifically, the radial sampling density of both the projections and the reconstructed image decreases exponentially with increasing distance from the ROI. The problem and data are reminiscent of the recently formulated local tomography problem; however, the authors' algorithm reconstructs the ROI of the image itself, not the filtered version of it obtained using local tomography. The new algorithm has the added advantages of speed (it can be implemented entirely using the FFT) and parallelizability (each image harmonic is computed independently). Numerical examples compare the new algorithm to filtered backprojection.     

Analytical formulae for reconstruction of certain discrete signalsfrom phase level and line crossings

We provide simple and explicit formulae for reconstructing any member of a class of discrete-time signals from the frequencies at which its Fourier phase crosses any specific level of constant phase or a linear-phase line with integer slope, provided that the number of crossings equals the length of the signal support. Unlike previous closed-form solutions, solution of an ill-conditioned system of linear equations is not required. The associated uniqueness results reduce, in special cases, to previous results for reconstruction from Fourier transform real and imaginary part zero crossings