Algorithms And Applications Of Underdetermined Semi-blind Source Separation

During the past decade, blind source separation (BSS) has become an active branch of digital signal processing. Owing to its specific advantage of weak request for prior information, BSS has been applied to many fields such as wireless communication, biomedical signals processing, and geological exploration. However, BSS has some disadvantages due to utilizing no prior information, such as ambiguous order of the estimations. As such, BSS utilizing prior information, namely semi-blind BSS, has been proposed recently and demonstrated considerable promise in improving its performance.However, semi-blind methods are mainly used in conventional BSS (there are more mixtures than sources) as reported by the publications. Since the underdetermined BSS (more sources than mixtures) has been gaining increasing attention, there is a need to develop semi-blind methods for underdetermined BSS by utilizing prior information about the source signals. Therefore, we proposed in this paper two semi-blind algorithms for estimating sparse sources in the underdetermined case and then utilizing the proposed methods to analyze the security of a BSS-based encryption. The main work of this thesis is as follows:(1) We proposed an underdetermined blind extraction algorithm for sparse sources based on mixture segmentation. The mixed signals were first divided into multiple segments according to three different cases of characteristics. The segments were then processed in different ways. The desired estimation was finally extracted by measuring its closeness with a reference signal constructed with prior information. We carried out computer simulations with synthesized periodic sparse signals. Simulation results show the efficacy of the proposed method.(2) We proposed a semi-blind expectation-maximization (EM) algorithm for estimating sparse sources in the underdetermined case. EM algorithm is an effective method for underdetermined BSS. In order to further improve its performance, we incorporated prior information about some signals of interest into the cost function of the EM algorithm. Simulation results demonstrate that the desired signals can be recovered in a predefined order with excellent performance.(3) We finally used the semi-blind underdetermined BSS algorithms to analyze a BSS-based encryption method, which utilized the underdetermined BSS problem to ensure it's security. We tried to attack the BSS-based encryption with three underdetermined BSS algorithms (one of them is semi-blind underdetermined BSS) without key signals. Simulation results demonstrate that the encrypting method is safe under the semi-blind underdetermined BSS attacks.