A fundamental imaging problem in microstructural analysis of metals is the reconstruction of local crystallographic orientations from X-ray diffraction measurements. This work develops a fast, accurate, and robust method for the computation of the three-dimensional orientation distribution function for individual grains of the material in consideration. We study two iterative large-scale reconstruction algorithms, the algebraic reconstruction technique (ART) and conjugate gradients for least squares (CGLS), and demonstrate that right preconditioning is necessary in both algorithms to provide satisfactory reconstructions. Our right preconditioner is not a traditional one that accelerates convergence; its purpose is to modify the smoothness properties of the reconstruction. We also show that a new stopping criterion, based on the information available in the residual vector, provides a robust choice of the number of iterations for these preconditioned methods.

We develop a computationally efficient algorithm for the problem of anisotropic smoothing in images, i.e., smoothing an image along its directional fields. Whereas similar problems are often posed and solved as PDE problems in the literature, we formulate the problem as a convex programming problem. We present efficient implementations of interior-point algorithms for solving large instances of this problem.

The signal subspace approach for non-parametric speech enhancement is considered. Several algorithms have been proposed in the literature but only partly analyzed. Here, the different algorithms are compared, and the emphasis is put onto the limiting factors and practical behavior of the estimators. Experimental results show that the signal subspace approach may lead to a significant enhancement of the signal to noise ratio of the output signal.

We consider an algorithm for reduction of broadband noise in speech based on signal subspaces. The algorithm is formulated by means of the quotient singular value decomposition (QSVD). With this formulation, a prewhitening operation becomes an integral part of the algorithm. We demonstrate that this is essential in connection with updating issues in real-time recursive applications. We also illustrate by examples that we are able to achieve a satisfactory quality of the reconstructed signal.

This paper presents FORTRAN 77 implementations of the lookahead Levinson algorithm of Chan and Hansen (7, 8) for solving symmetric indefinite and general Toeplitz systems. The algorithms are numerically stable for all Toeplitz matrices that do not have many consecutive ill-conditioned leading principal submatrices, and also produce estimates of the algorithm and matrix condition numbers. In contrast, the classical Levinson algorithm is only guaranteed to be numerically stable for symmetric positive definite Toeplitz matrices, and no condition estimate is produced.

In many fields of signal and image processing control, and telecommunication there is much interest today in the numerical techniques offered by linear algebra. The singular value decomposition (SVD) is one of the techniques which have proven useful in many engineering applications, but unfortunately its computation is a costly procedure. The QR factorization (QRF) requires much less computational effort, but rank and null-space estimates are not necessarily reliable. This paper presents a version of rank revealing QR (RRQR) algorithm which is suited for implementation on a VLSI systolic array. The implementation of the RRQRF requires n(n+1)/2 processors and O(n) external buffers, for a problem of order n. The execution time for the algorithm is O(nr), where r is A's numerical rank.>

This paper presents FORTRAN 77 implementations of the lookahead Levinson algorithm of Chan and Hansen [7, 8] for solving symmetric indefinite and general Toeplitz systems. The algorithms are numerically stable for all Toeplitz matrices that do not have manyconsecutiveill-conditioned leading principal submatrices, and also produce estimates of the algorithm and matrix condition numbers. In contrast, the classical Levinson algorithm is only guaranteed to be numerically stable for symmetric positive definite Toeplitz matrices, and no condition estimate is produced.