The sparse coding is approximation/representation of signals with the minimum number of coefficients using an overcomplete set of elementary functions. This kind of approximations/ representations has found numerous applications in source separation, denoising, coding and compressed sensing. The adaptation of the sparse approximation framework to the coding problem of signals is investigated in this thesis. Open problems are the selection of appropriate models and their orders, coefficient quantization and sparse approximation method. Some of these questions are addressed in this thesis and novel methods developed. Because almost all recent communication and storage systems are digital, an easy method to compute quantized sparse approximations is introduced in the first part. The model selection problem is investigated next. The linear model can be adapted to better fit a given signal class. It can also be designed based on some a priori information about the model. Two novel dictionary selection methods are separately presented in the second part of the thesis. The proposed model adaption algorithm, called Dictionary Learning with the Majorization Method (DLMM), is much more general than current methods. This generality allowes it to be used with different constraints on the model. Particularly, two important cases have been considered in this thesis for the first time, Parsimonious Dictionary Learning (PDL) and Compressible Dictionary Learning (CDL). When the generative model order is not given, PDL not only adapts the dictionary to the given class of signals, but also reduces the model order redundancies. When a fast dictionary is needed, the CDL framework helps us to find a dictionary which is adapted to the given signal class without increasing the computation cost so much. Sometimes a priori information about the linear generative model is given in format of a parametric function. Parametric Dictionary Design (PDD) generates a suitable dictionary for sparse coding using the parametric function. Basically PDD finds a parametric dictionary with a minimal dictionary coherence, which has been shown to be suitable for sparse approximation and exact sparse recovery. Theoretical analyzes are accompanied by experiments to validate the analyzes. This research was primarily used for audio applications, as audio can be shown to have sparse structures. Therefore, most of the experiments are done using audio signals.

Since the publication of Dr. Johnson’s first English dictionary in 1755, there have been rapid changes in the development of dictionaries in other parts of the world. However, the advances are perceived more in other languages of the world such as the European languages while in Africa, the changes have been very slow. The majority of dictionaries utilised by most Africans are bilingual and were produced by the missionaries. These dictionaries were aimed at serving the needs of the missionaries, but more recently African scholars have been trying to create dictionaries that are intended to meet the needs of the native speakers particularly because the existing dictionaries contain many words which are archaic or going out of use. This means that the currently produced dictionaries should reflect the changes that have occurred in languages and society. The two dictionaries under scrutiny, Sesuto-English Dictionary and Sethantšo sa Sesotho, share similar content as if they were both targeting the same generation even though the former was written by missionaries in the 19th century while the latter was created by a Sesotho native speaker in the 21st century. This study aimed to establish whether the two dictionaries are the same or not, or whether Sethantšo sa Sesotho had been derived from Sesuto-English Dictionary as well as whether the two dictionaries meet the needs of the contemporary users. The study employed adaptation theory in order to discover the originality of Sethantšo sa Sesotho. User-perspective approach and communication-oriented function were utilised to judge the effectiveness of the two dictionaries in reading and writing and to analyse users’ views. The study established that Sethantšo sa Sesotho has adapted 69% lexical items from Sesuto-English Dictionary; words are arranged in a similar order in both dictionaries with slight differences here and there; most definitions and illustrative phrases/sentences are the same even though the author of Sethantšo sa Sesotho did not acknowledge using any written source of information, thus violating the principles of adaptation; use of these dictionaries during reading and writing was found to be beneficial to users; and both dictionaries lack current words which users encounter daily. / African Languages / D. Litt. et Phil.(African Languages)