## Advances in zero-based consistent deconvolution and evaluation of human sensory-motor function (1994)

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##### Type of Content

Theses / Dissertations##### UC Permalink

https://hdl.handle.net/10092/100170##### Thesis Discipline

Electrical Engineering##### Degree Name

Doctor of Philosophy##### Publisher

University of Canterbury##### Language

English##### Collections

##### Abstract

Work in two separate research areas is presented. The two areas are the development of a new two-dimensional (2-D) zero-based deconvolution algorithm and the evaluation of human sensory-motor (S-M) function in a 2-D environment.

In Part One of this thesis the new algorithm which solves the 2-D standard deconvolution problem (i.e. deconvolution of a single contaminated blurred image when the point spread function (psf) is known a priori) is described. The algorithm performs the deconvolution by separating a subset of the zeros of the Z transform of the convolution into two further subsets. This separation is performed by using the zeros of the psf to recognise and eliminate, from the set of convolution zeros, the set of zeros that pertain to the psf actually responsible for the blurring. The remaining subset of zeros characterise the original image and an estimate of the original image can be reconstructed from these zeros by using an algebraic technique. As this technique does not explicitly use the psf to generate the image estimate (unlike existing deconvolution techniques such as inverse and Wiener filtering) it was anticipated that the quality of the reconstructions obtained would not be strongly dependent on the psf estimate accuracy.

The performance of the new zero-based deconvolution algorithm has been extensively assessed. It has been foW1d that the algorithm can successfully deblur small (original image sizes < 16 x 16 pixels), high SNR (2 40 dB) blurred images. On comparing the quality of the reconstructions provided by this new algorithm to those provided by the Wiener filter, it was found that the image estimate quality of the new algorithm was less dependent on the psf accuracy than that of the Wiener filter. The effects of contamination on the position of the zeros in Z space has also been investigated. In the situation where the contamination is band-limited, it is shown that specific zeros are likely to be affected more by the contamination than others. It is shown that this knowledge can be used, in the band-limited case, to improve the quality of the reconstructions provided by the new algorithm. In comparison to existing techniques, such as the Wiener filter, this algorithm is computationally very expensive and this computational expense becomes prohibitive as the image size increases. It appears that the section of the algorithm responsible for the large computational expense and which limits the ability of the algorithm to obtain useful reconstructions from larger images is the reconstruction section, as opposed to the zero recognition and separation section. Possible techniques that could be used to improve the algorithm's performance in these two areas are described.

The phase retrieval problem is a problem very similar to deconvolution. The success of the new algorithm at solving the deconvolution problem prompted the development of a zero based algorithm which can be used to assist the convergence of one of the iterative algorithms typically used to solve the phase retrieval problem. It is shown that the zero-based algorithm can successfully assist the iterative algorithm in obtaining a solution, however the zero-based algorithm's enormous computational cost results in no overall computational saving.

In Part Two two new 2-D eye-arm pursuit tracking tasks, which have been developed to facilitate the investigation of human S-M function in a 2-D environment, are described. The tracking tasks assess a subject's ability to accurately follow a moving visual target with a pointer controlled by the coordinated movement of an upper limb. One of the tracking tasks uses a smoothly changing pseudo-random target signal and the other uses a signal consisting of temporally and spatially unpredictable steps. The 2-D tasks were developed with the anticipation that they might provide more sensitive measures than their 1-D counterparts of, as well as additional information on, both abnormal and normal S-M function. Two trials where conducted to detennine what benefits the new 2-D tracking tasks could provide. It was found that the 2-D tasks could successfully demonstrate the deficits known to occur in the Parkinsonian S-M system and that the 2-D tasks could detect these deficits with a marginally greater sensitivity than 1-D tasks. It was also found that on going from a 1-D to a 2-D tracking task, the observed degradation in tracking performance consists of two components. The first component is due to an increase in the S-M system processing delay when tracking multidimensional signals and the second is due to a reduction in tracking accuracy with any increase in average task displacement and/or velocity. An age dependent difference between the subject's performance in the vertical and horizontal directions of the 2-D tracking task was also observed.

One of the main performance measures used with tracking tasks is the time delay between the target moving and the S-M system responding. An evaluation of the accuracy of the various techniques which can be used to calculate the time delay has been conducted. Of the five techniques tested, it was found that the standard cross-correlation technique or the least squares time delay estimation technique could provide the most accurate estimates of the time delay. The reasons for the inaccuracies in the time delay estimates provided by some of the other techniques in the comparison are also explained.