Sıkıştırmalı algılama matrisleri için yeni tasarım yontemi

In this thesis, we studied the mathematical foundations of Compressive Sensing. Compressive Sensing is an area which gives us more ability than Nyquist-Shannon Theorem with an extra condition: Sparsity. If a signal is sparse, we can recover the signal using fewer measurements than the required in Nyquist-Shannon Theorem. Firstly, we examined the necessary conditions to use compressive sensing for recovery. Sparsity is the key to use compressive sensing for signal recovery. Besides, we look into the relationship between sparsity of a signal and sensing matrices. Then, we look into recovery algorithms, sensing matrix design methods and properties of sensing matrices. Two most imporant properties of sensing matrices are Null Space Property and Restricted Isometry Property. We also examined the relationship between Null Space Property and Restricted Isometry Property. Later, we made experiments using different sensing matrix generation methods. Lastly, we propose a novel design for sensing matrix generation and compared the results of these experiments with the other sensing matrix design methods using different recovery algorithms.