Michael P. Ekstrom

Two-dimensional spectral factorization with applications in recursive digital filtering

The concept of spectral factorization is extended to two dimensions in such a way as to preserve the analytic characteristics of the factors. The factorization makes use of a homomorphic transform procedure due to Wiener. The resulting factors are shown to be recursively computable and stable in agreement with one-dimensional (1-D) spectral factorization. The factors are not generally two-dimensional (2-D) polynomials, but can be approximated as such. These results are applied to 2-D recursive filtering, filter design, and a computationally attractive stability test for recursive filters.

Two-dimensional recursive filter design--A spectral factorization approach

This paper concerns development of an efficient method for the design of two-dimensional (2-D) recursive digital filters. The specific design problem addressed is that of obtaining half-plane recursive filters which satisfy prescribed frequency response characteristics. A novel design procedure is presented which incorporates a spectral factorization algorithm into a constrained, nonlinear optimization approach. A computational implementation of the design algorithm is described and its design capabilities demonstrated with several examples.

A stability test for 2-D recursive digital filters using the complex cepstrum

A procedure is presented for testing the stability of 2-D recursive filters. This test is based on the mapping properties of the complex cepstrum. A numerical algorithm for computing the 2-D cepstrum is described, and subsequently used in calculating numerical examples of the stability test.

A Numerical Algorithm for Identifying Spread Functions of Shift-Invariant Imaging Systems

Numerical optimization techniques are applied to the identification of linear, shift-invariant imaging systems in the presence of noise. The approach used is to model the available or measured image of a real known object as the planar convolution of object and system-spread function and additive noise. The spread function is derived by minimization of a spatial error criterion (least squares) and characterized using a matric formalism. The numerical realization of the algorithm is discussed in detail; the most substantial problem encountered being the calculation of a vector-generalized inverse. This problem is avoided in the special case where the object scene is taken to be decomposable.

Design of stable 2-D half-plane recursive filters using spectral factorization

In this paper a new design algorithm for two-dimensional (2-D) recursive digital filters is presented, with emphasis on the general class of half-plane filters. A recently developed 2-D spectral factorization procedure and a nonlinear optimization algorithm are incorporated to iteratively converge to a stable, (locally) optimum filter. Details of the computations required in the implementation of the design procedure are presented, in addition to an example of its application.

Best Linear Decoding of Random Mask Images

In 1968 Dicke proposed coded imaging of x and ¿ rays via random pinholes. Since then, many authors have agreed with him that this technique can offer significant image improvement. We present a best linear decoding of the coded image and show its superiority over the conventional matched filter decoding. Experimental results in the visible light region are presented.

Why filter recursively in two dimensions

The relative advantages of 2-D recursive digital filters over their nonrecursive counterparts are discussed. A design example illustrates the ability of 2-D recursive filters to yield excellent responses with far fewer coefficients than nonrecursive filters require. This difficulty is seen to be partially overcome by using nonrecursive filters with very efficient implementations.

Digital image processing at Lawrence Livermore Laboratory part I — Diagnostic radiography applications

In recent years there has been an increasing interest in the processing of pictorial images by digital computer. Since the initial success of digital image correction at JPL in support of the space program, considerable effort has been devoted to applying image processing techniques in a wide variety of application areas. This effort has involved the direct spin-off of some basic research results in industrial applications and the utilization of this experience in establishing relevant directions of new image processing research and development.

Multidimensional spectral factorization

In this paper, we present a procedure for the spectral factorization of multidimensional spectral density functions. Properties of the multidimensional cepstrum are developed and used as a basis for the procedure. In analogy with Wieners one-dimensional factorization, the resulting factors are stable and realizable (i.e., recursible). A numerical algorithm for performing the factorization is described, along with its use in obtaining unilateral representations of multidimensional random fields.

A Monte Carlo approach to numerical deconvolution

In this paper, a numerical procedure for solving deconvolution problems is presented. The procedure is based on the Monte-Carlo method which statistically estimates each element in the deconvolved excitation. A discrete Fourier transform technique is used to improve the quality of these estimates for a prescribed amount of computation.