The purpose of this thesis is to develop a mathematical approach and associated software implementation for deconvolution of two-dimensional Transmission Electron Microscope (TEM) images. The focus is on TEM images of weakly scattering amorphous biological specimens that mainly produce phase contrast. The deconvolution is to remove the distortions introduced by the TEM detector that are modeled by the Modulation Transfer Function (MTF). The report tests deconvolution of the TEM detector MTF by Wiener _ltering and Tikhonov regularization on a range of simulated TEM images with varying degree of noise.The performance of the two deconvolution methods are quanti_ed by means of Figure of Merits (FOMs) and comparison in-between methods is based on statistical analysis of the FOMs.

Axicons have been proposed for imaging applications since they offer the advantage of extended depth of field (DOF). This enhanced DOF comes at the cost of degraded image quality. Image processing has been proposed to improve the image quality. Initial efforts were focused on the use of an axicon in a borescope thereby extending depth of focus and eliminating the need for a focusing mechanism. Though promising, it is clear that image processing would lead to improved image quality. This would also eliminate the need, in certain applications, for a fiber optic imaging bundle as many modern day video borescopes use an imaging sensor coupled directly to the front end optics. In the present work, three types of refractive axicons are examined: a linear axicon, a logarithmic axicon and a Fresnel axicon. The linear axicon offers the advantage of simplicity and a significant amount of scientific literature including the application of image restoration techniques. The Fresnel axicon has the advantage of compactness and potential low cost of production. As no physical prior examples of the Fresnel axicons were available for experimentation until recently, very little literature exists. The logarithmic axicon has the advantage of nearly constant longitudinal intensity distribution and an aspheric design producing superior pre-processed images over the aforementioned elements. Point Spread Functions (PSFs) for each of these axicons have been measured. These PSFs form the basis for the design of digital image restoration filters. The performance of these three optical elements and a number of restoration techniques are demonstrated and compared.

<p>Signal processing within the neurophysiological field is challenging and requires short processing time and reliable results. In this thesis, three main problems are considered.</p><p>First, a modified line source model for simulation of muscle action potentials (APs) is presented. It is formulated in continuous-time as a convolution of a muscle-fiber dependent transmembrane current and an electrode dependent weighting (impedance) function. In the discretization of the model, the Nyquist criterion is addressed. By applying anti-aliasing filtering, it is possible to decrease the discretization frequency while retaining the accuracy. Finite length muscle fibers are incorporated in the model through a simple transformation of the weighting function. The presented model is suitable for modeling large motor units.</p><p>Second, the possibility of discerning the individual AP components of the concentric needle electromyogram (EMG) is explored. Simulated motor unit APs (MUAPs) are prefiltered using Wiener filtering. The mean fiber concentration (MFC) and jitter are estimated from the prefiltered MUAPs. The results indicate that the assessment of the MFC may well benefit from the presented approach and that the jitter may be estimated from the concentric needle EMG with an accuracy comparable with traditional single fiber EMG.</p><p>Third, automatic, rather than manual, detection and discrimination of recorded C-fiber APs is addressed. The algorithm, detects the Aps reliably using a matched filter. Then, the detected APs are discriminated using multiple hypothesis tracking combined with Kalman filtering which identifies the APs originating from the same C-fiber. To improve the performance, an amplitude estimate is incorporated into the tracking algorithm. Several years of use show that the performance of the algorithm is excellent with minimal need for audit.</p>

Signal processing within the neurophysiological field is challenging and requires short processing time and reliable results. In this thesis, three main problems are considered. First, a modified line source model for simulation of muscle action potentials (APs) is presented. It is formulated in continuous-time as a convolution of a muscle-fiber dependent transmembrane current and an electrode dependent weighting (impedance) function. In the discretization of the model, the Nyquist criterion is addressed. By applying anti-aliasing filtering, it is possible to decrease the discretization frequency while retaining the accuracy. Finite length muscle fibers are incorporated in the model through a simple transformation of the weighting function. The presented model is suitable for modeling large motor units. Second, the possibility of discerning the individual AP components of the concentric needle electromyogram (EMG) is explored. Simulated motor unit APs (MUAPs) are prefiltered using Wiener filtering. The mean fiber concentration (MFC) and jitter are estimated from the prefiltered MUAPs. The results indicate that the assessment of the MFC may well benefit from the presented approach and that the jitter may be estimated from the concentric needle EMG with an accuracy comparable with traditional single fiber EMG. Third, automatic, rather than manual, detection and discrimination of recorded C-fiber APs is addressed. The algorithm, detects the Aps reliably using a matched filter. Then, the detected APs are discriminated using multiple hypothesis tracking combined with Kalman filtering which identifies the APs originating from the same C-fiber. To improve the performance, an amplitude estimate is incorporated into the tracking algorithm. Several years of use show that the performance of the algorithm is excellent with minimal need for audit.