Theory and realization of novel algorithms for random sampling in digital signal processing

Random sampling is a technique which overcomes the alias problem in regular sampling. The randomization, however, destroys the symmetry property of the transform kernel of the discrete Fourier transform. Hence, when transforming a randomly sampled sequence to its frequency spectrum, the Fast Fourier transform cannot be applied and the computational complexity is N(^2). The objectives of this research project are (1) To devise sampling methods for random sampling such that computation may be reduced while the anti-alias property of random sampling is maintained : Two methods of inserting limited regularities into the randomized sampling grids are proposed. They are parallel additive random sampling and hybrid additive random sampling, both of which can save at least 75% of the multiplications required. The algorithms also lend themselves to the implementation by a multiprocessor system, which will further enhance the speed of the evaluation. (2) To study the auto-correlation sequence of a randomly sampled sequence as an alternative means to confirm its anti-alias property : The anti-alias property of the two proposed methods can be confirmed by using convolution in the frequency domain. However, the same conclusion is also reached by analysing in the spatial domain the auto-correlation of such sample sequences. A technique to evaluate the auto-correlation sequence of a randomly sampled sequence with a regular step size is proposed. The technique may also serve as an algorithm to convert a randomly sampled sequence to a regularly spaced sequence having a desired Nyquist frequency. (3) To provide a rapid spectral estimation using a coarse kernel : The approximate method proposed by Mason in 1980, which trades the accuracy for the speed of the computation, is introduced for making random sampling more attractive. (4) To suggest possible applications for random and pseudo-random sampling : To fully exploit its advantages, random sampling has been adopted in measurement Random sampling is a technique which overcomes the alias problem in regular sampling. The randomization, however, destroys the symmetry property of the transform kernel of the discrete Fourier transform. Hence, when transforming a randomly sampled sequence to its frequency spectrum, the Fast Fourier transform cannot be applied and the computational complexity is N"^. The objectives of this research project are (1) To devise sampling methods for random sampling such that computation may be reduced while the anti-alias property of random sampling is maintained : Two methods of inserting limited regularities into the randomized sampling grids are proposed. They are parallel additive random sampling and hybrid additive random sampling, both of which can save at least 75% , of the multiplications required. The algorithms also lend themselves to the implementation by a multiprocessor system, which will further enhance the speed of the evaluation. (2) To study the auto-correlation sequence of a randomly sampled sequence as an alternative means to confirm its anti-alias property : The anti-alias property of the two proposed methods can be confirmed by using convolution in the frequency domain. However, the same conclusion is also reached by analysing in the spatial domain the auto-correlation of such sample sequences. A technique to evaluate the auto-correlation sequence of a randomly sampled sequence with a regular step size is proposed. The technique may also serve as an algorithm to convert a randomly sampled sequence to a regularly spaced sequence having a desired Nyquist frequency. (3) To provide a rapid spectral estimation using a coarse kernel : The approximate method proposed by Mason in 1980, which trades the accuracy for the speed of the computation, is introduced for making random sampling more attractive. (4) To suggest possible applications for random and pseudo-random sampling : To fully exploit its advantages, random sampling has been adopted in measurement instruments where computing a spectrum is either minimal or not required. Such applications in instrumentation are easily found in the literature. In this thesis, two applications in digital signal processing are introduced. (5) To suggest an inverse transformation for random sampling so as to complete a two-way process and to broaden its scope of application. Apart from the above, a case study of realizing in a transputer network the prime factor algorithm with regular sampling is given in Chapter 2 and a rough estimation of the signal-to-noise ratio for a spectrum obtained from random sampling is found in Chapter 3. Although random sampling is alias-free, problems in computational complexity and noise prevent it from being adopted widely in engineering applications. In the conclusions, the criteria for adopting random sampling are put forward and the directions for its development are discussed

Extracting root system architecture from X-ray micro computed tomography images using visual tracking

X-ray micro computed tomography (µCT) is increasingly applied in plant biology as an imaging system that is valuable for the study of root development in soil, since it allows the three-dimensional and non-destructive visualisation of plant root systems. Variations in the X-ray attenuation values of root material and the overlap in measured intensity values between roots and soil caused by water and organic matter represent major challenges to the extraction of root system architecture. We propose a novel technique to recover root system information from X-ray CT data, using a strategy based on a visual tracking framework embedding a modiffed level set method that is evolved using the Jensen-Shannon divergence. The model-guided search arising from the visual tracking approach makes the method less sensitive to the natural ambiguity of X-ray attenuation values in the image data and thus allows a better extraction of the root system. The method is extended by mechanisms that account for plagiatropic response in roots as well as collision between root objects originating from different plants that are grown and interact within the same soil environment. Experimental results on monocot and dicot plants, grown in different soil textural types, show the ability of successfully extracting root system information. Various global root system traits are measured from the extracted data and compared to results obtained with alternative methods

Extracting root system architecture from X-ray micro computed tomography images using visual tracking

X-ray micro computed tomography (µCT) is increasingly applied in plant biology as an imaging system that is valuable for the study of root development in soil, since it allows the three-dimensional and non-destructive visualisation of plant root systems. Variations in the X-ray attenuation values of root material and the overlap in measured intensity values between roots and soil caused by water and organic matter represent major challenges to the extraction of root system architecture. We propose a novel technique to recover root system information from X-ray CT data, using a strategy based on a visual tracking framework embedding a modiffed level set method that is evolved using the Jensen-Shannon divergence. The model-guided search arising from the visual tracking approach makes the method less sensitive to the natural ambiguity of X-ray attenuation values in the image data and thus allows a better extraction of the root system. The method is extended by mechanisms that account for plagiatropic response in roots as well as collision between root objects originating from different plants that are grown and interact within the same soil environment. Experimental results on monocot and dicot plants, grown in different soil textural types, show the ability of successfully extracting root system information. Various global root system traits are measured from the extracted data and compared to results obtained with alternative methods

The Effect of Emotional Intelligence Training via Method Psychodrama on Marital Satisfaction of Patients with MS

MS is a progressive and chronic disease of the central nervous system with symptoms that can be debilitating. Appropriate interventions including Emotional Intelligence Training improve the quality of life MS patients. The aim of this study is to determine the effect of emotional intelligence training through Psycho-Drama methods on marital satisfaction of patients with MS. This study is a one-group, before-after, quasi-experimental study. A total of 22 patients were enrolled in this study. The samples were selected through non-random sampling based on the goal of study among visitors of MS Society, Kurdistan province, Iran. Data collection tool was questionnaires with two sections: 1) demographic information and 2) ENRICH-B marital satisfaction questionnaire including 47 items. Intervention was conducting 20 sessions of 2-hour training. Questionnaires were filled by patients before and after intervention. Methods for data analysis were descriptive statistics (tables of relative frequency distribution, the mean, and standard deviation) and inferential statistics of paired t test. Paired t test showed a significant difference in total scores of marital satisfaction before and after training sessions (P < 0.05). Finally, we concluded that, designing and applying emotional intelligence training programs via psychodrama method is effective on marital satisfaction in patients with multiple sclerosis. Keywords: Multiple sclerosis, emotional intelligence training, psychodrama, marital satisfactio