Matrix Designs and Methods for Secure and Efficient Compressed Sensing

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique?s foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of natural signals with minimum complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption. In this context, we also show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content. Finally, we explore the application of compressed sensing in the design of a multispectral imager by implementing an optical scheme for compressive imaging. This design entails a coded aperture array and Fabry-P?rot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement in terms of an accurate calibration of the sensing matrix as applied by the devised imager at the optical level.