A new approach to the analysis of the structural properties of multivariable convolutional codes over finite fields is presented. It is based on the properties of the state transition graph which can be considered as a generalization to the multivariable case of the classical Good-De-Bruijn graph associated with linear shift register sequences. The concept of a minimal graph is introduced and shown to be isomorphic to the class of all minimal encoders previously defined by Forney. Straightforward algorithms based on simple algebraic and graph manipulations are introduced to allow for the reduction of any state transition graph to a minimal form. Furthermore each stage in the reduction procedure is shown to be related to some fundamental system theoretic concept including the conditions for causal invertibility, pseudo invertibility and polynomial invertibility of a linear feedforward system. By using the concept of dual codes and introducing a straightforward algorithm for the construction of a dual encoder in minimal form which is valid on any field; a simple procedure is further devised providing for the reduction of any rational basis to a minimal polynomial form and the applications of this result to multivariable realization theory are discussed. Finally several non exhaustive applications of the above mentioned concepts to linear system theory are developed. A special emphasis is placed on the solution of the problem associated with the construction of the class of all minimal order, minimal delay pseudo inverses of any realizable linear system. Furthermore, we present a solution to the minimal partial realization problem for vectored sequences based on the use of a Berlekamp-Massey type algorithm.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 73-75). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 73-75). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 76-79). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 76-79). Also available on the Internet.

Image processing consists of a series of tasks which widely appear in many areas. It can be used for processing photos taken by people's cameras, astronomy radio, radar imaging, medical devices and tomography. Among these tasks, image segmentation is a fundamental task in a series of applications. Image segmentation is so important that it attracts hundreds of thousands of researchers from lots of fields all over the world. Given an image, the goal of image segmentation is to classify all pixels into several classes. Given an image defined over a domain, the segmentation task is to divide the domain into several different sub-domains such that pixels in each sub-domain share some common information. Variational methods showcase their performance in all kinds of image processing problems, such as image denoising, image debluring, image segmentation and so on. They can preserve structures of images well. In recent decades, it is more and more popular to reformulate an image processing problem into an energy minimization problem. The problem is then minimized by some optimization based methods. Meanwhile, convolutional neural networks (CNNs) gain outstanding achievements in a wide range of fields such as image processing, nature language processing and video recognition. CNNs are data-driven techniques which often need large datasets for training comparing to other methods like variational based methods. When handling image processing tasks with large scale datasets, CNNs are the first selections due to their superior performances. However, the class of each pixel is predicted independently in semantic segmentation tasks which are dense classification problems. Spatial regularity of the segmented objects is still a problem for these methods. Especially when given few training data, CNNs could not perform well in the details. Isolated and scattered small regions often appear in all kinds of CNN segmentation results. In this thesis, we successfully add spatial regularization to the segmented objects. In our methods, spatial regularization such as total variation (TV) can be easily integrated into CNNs and they produce smooth edges and eliminates isolated points. Spatial dependency is a very important prior for many image segmentation tasks. Generally, convolutional operations are building blocks that process one local neighborhood at a time, which means CNNs usually don't explicitly make use of the spatial prior on image segmentation tasks. Empirical evaluations of the regularized neural networks on a series of image segmentation datasets show its good performance and ability in improving the performance of many image segmentation CNNs. We also design a recurrent structure which is composed of multiple TV blocks. By applying this structure to a popular segmentation CNN, the segmentation results are further improved. This is an end-to-end framework to regularize the segmentation results. The proposed framework could give smooth edges and eliminate isolated points. Comparing to other post-processing methods, our method needs little extra computation thus is effective and efficient. Since long range dependency is also very important for semantic segmentation, we further present non-local regularized softmax activation function for semantic image segmentation tasks. We introduce graph operators into CNNs by integrating nonlocal total variation regularizer into softmax activation function. We find the non-local regularized softmax activation function by the primal-dual hybrid gradient method. Experiments show that non-local regularized softmax activation function can bring regularization effect and preserve object details at the same time

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M.Ing. / In practical transmission or storage systems, the convolutional encoding and Viterbi decoding scheme is widely used to protect the data from substitution errors. Two independent insertion/deletion/substitution (IDS) error correcting designs, working on the convolutional encoder and the Viterbi decoder respectively, are shown in this thesis. The Levenshtein distance has previously been postulated to be a suitable branch comparison metric for the Viterbi algorithm on channels with not only substitution errors, but also insertion/deletion errors. However, to a large extent, this hypothesis has still to be investigated. In the first coding scheme, a modified Viterbi algorithm based on the Levenshtein distance metric is used as the decoding algorithm. Our experiments give evidence that the modified Viterbi algorithm with the Levenshtein distance metric is suitable as an applicable decoding algorithm for IDS channels. In the second coding scheme, a new type of convolutional code called the path-pruned convolutional code is introduced on the encoder side. By periodically deleting branches in a high rate convolutional code trellis diagram to create a specific insertion/deletion error correcting block codeword structure in the encoded sequence, we can obtain an encoding system to protect against insertion, deletion and substitution errors at the same time. Moreover, the path-pruned convolutional code is an ideal code to use for unequal error protection. Therefore, we also present an application of the rate-compatible path-pruned convolutional codes over IDS channels.