RBFN restoration of nonlinearly degraded images.

We investigate a technique for image restoration using nonlinear networks based on radial basis functions. The technique is also based on the concept of training or learning by examples. When trained properly, these networks are used as spatially invariant feedforward nonlinear filters that can perform restoration of images degraded by nonlinear degradation mechanisms. We examine a number of network structures including the Gaussian radial basis function network (RBFN) and some extensions of it, as well as a number of training algorithms including the stochastic gradient (SG) algorithm that we have proposed earlier. We also propose a modified structure based on the Gaussian-mixture model and a learning algorithm for the modified network. Experimental results indicate that the radial basis function network and its extensions can be very useful in restoring images degraded by nonlinear distortion and noise.

Array redundancy for active line arrays.

Active imaging arrays are used to image scenes composed of reflectors of transmitted radiation, and in many such applications, line arrays are employed. In this paper, we discuss scanned active line arrays for imaging based on image synthesis. We define the novel concept of array redundancy for active arrays, analogous to the well-known concept of redundancy applied to passive arrays, and we define and give examples of minimum redundancy and reduced redundancy line arrays composed of transmit/receive elements. Such arrays differ from their passive imaging counterparts both in geometry and in element count.

A structure for adaptive order statistics filtering.

In applications such as smoothing and enhancement of images, adaptive filtering techniques offer the flexibility needed for good performance with non-stationary observations. Many adaptive schemes can be based on the idea of determining the local statistics of the signal through appropriate tests on the data, to aid in the selection of a filtering procedure that is suited to the data. In the paper, the authors consider decision-directed or data-dependent adaptive filtering schemes that are based on order statistics. A general formulation for such a class of adaptive order statistics filters is presented. Approximate statistical performance analysis, especially in the presence of edges, may be carried out for this entire class of filters. The authors give examples of some existing filters that fit into this framework. The formulation also accommodates filters that employ multiple windows in their operation. To illustrate the potential of this class of multiple window (MW) filters, they construct and analyze simple filters, like the triple window median (TW-MED) and the triple window median of means (TW-MOM) filters, that are shown to yield useful performance. The class of mean-median hybrid (MMH) filters is also presented as a simple example which may be extended to give interesting performance.

Coarray synthesis with circular and elliptical boundary arrays.

An elliptical boundary aperture is a collection of points lying on an ellipse from which energy is transmitted and/or received. An important special case is the circular boundary aperture. When these apertures are used with beamforming to produce a narrowband image of a far-field source, the corresponding point spread function (PSF) is characterized by high sidelobes. The concept of the coarray of an imaging system is used here to develop techniques which synthesize the effect of a more desirable PSF with an elliptical boundary aperture. Techniques are given for use in active imaging of spatially coherent sources, as well as passive imaging of spatially incoherent sources. Discrete arrays and continuous apertures are considered separately. The approach shows that the PSF synthesis problem can be solved in many more ways than previously recognized, and this fact is exploited to develop procedures which have a least-squares optimality property.

High resolution coherent source location using transmit/receive arrays.

A general approach to super resolution imaging of point sources using active arrays of transmit/receive elements is presented. The usual techniques of high resolution imaging using single transmitters and passive receive arrays fail in the presence of sets of coherent point sources, which often arise due to coherent multipath. However, data obtained from transmit/receive arrays may be arranged into matrices to which eigenspace direction of arrival estimation may be successfully applied, even int he presence of coherent sources. Each such matrix may be thought of as corresponding to a different transmit/receive array; this may be either the actual transmit/receive array or a virtual transmit/receive array whose effect is synthesized. This approach provides great flexibility, since a large number of different synthetic or virtual arrays may be available for a given transmit/receive array, and each can provide a different tradeoff between the total number of resolvable targets and the largest number of mutually coherent targets which can be resolved.