Theoretical and practical aspects of image restoration and neurological signal processing are presented. All descriptions of algorithms are accompanied by examples.

All of the popular deconvolution algorithms that find application in image processing contexts are comprehensively reviewed, and inherent limitations of deconvolution are identified. Four categories of deconvolution algorithms are discussed in detail. The first category encompasses those conventional deconvolution techniques that are applicable in situations where estimates of the blurring function are available.

Ensemble blind deconvolution techniques, for situations in which many differently blurred versions of a single object are available, comprise the second category of deconvolution algorithms. Astronomical speckle processing, a collection of image processing techniques in optical and infrared astronomy for high spatial resolution imaging through the Earth's atmosphere, is the field in which ensemble blind deconvolution techniques find the most widespread application. Popular astronomical speckle imaging techniques are reviewed with one such technique, shift-and-add, and extensions to it, being examined in detail. Application of shift-and-add to fields other than astronomical speckle imaging are also outlined. Zero-and-add, a new en­semble blind deconvolution technique, is described in the context of one-dimensional astronomical speckle imaging. Zero-and-add compares the complex spectral zeros of the speckle images to identify the zeros common to all of the speckle images. From the common zeros a reconstruction of the object is computed. The effect upon the zero-and-add algorithm of contamination and windowing of speckle images is investigated. Extensions to zero-and-add allowing the technique to process two-dimensional speckle images are described. A composite method for processing one-dimensional infrared speckle images, which incorporates several image processing techniques including shift-and-add and zero-and-add, is introduced and invoked to process infrared speckle images of the astrometric binary star Ross 614 AB. This method automatically compensates for deficiencies in the scanning mechanism used to record infrared speckle images, and is self-calibrating for atmospheric effects.

The problem of reconstructing an image, or the phase of its spectrum, from its known spectral magnitude is called phase retrieval, which characterizes the third category of algorithms. This is a special subclass of the blind deconvolution problem in which the true image and blurring function are conjugate mirror images of each other. Iterative techniques implementing both phase retrieval, and the related problem of recovering the spectral magnitude from the phase, are reviewed. The direct phase retrieval algorithm (recently reported by R.G. Lane and co-workers), based on partitioning the complex spectral zeros of a convolution into the sets of zeros of the individual components, is examined. The effect of contamination upon this algorithm is investigated.

The status of the fourth category, which are general blind deconvolution algorithms capable of deconvolving a single blurred image without knowledge of the blurring function, is reviewed. A new iterative algorithm, capable of deconvolving the contaminated convolution of two components that can, in general, be complex, is introduced. The ability of general blind deconvolution algorithms to improve the image resulting from the shift-and-add algorithm is emphasised and illustrated.

The manifestation of epilepsy in the electroencephalogram of patients with suspected neurological disorders is outlined and a computerized system for the auto­ mated detection of this epileptiform activity is described. The system comprises two distinct stages. The first is a feature extractor, written in the conventional procedural language FORTRAN, which utilizes parts of previously published spike-detection algorithms to produce a list of all spike-like occurrences in the EEG. The second stage, written in the production system language OPS5, reads the list and employs rules incorporating knowledge elicited from an electroencephalographer (EEGer) to confirm or exclude each of the possible spikes. A summary of the detected epilepti-form events is produced which is available to the EEGer for interpreting the EEG. The performance of the expert system is compared with an EEGer reading (in the standard neurological fashion) a 320 second segment from an EEG containing epileptiform activity.