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 electrocardiographic tracks 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 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 that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager.

Radiocarbon and stable isotopes in the shell organic matrix: a new approach for the use of mollusk shells in the study of human evolution

Mollusk shells are often found in archeological sites, given their great preservation potential and high value as a multipurpose resource. They are often the only available material to use for radiocarbon dating, due to a lack of well-preserved bones in many archeological sites, especially for the key period of the Middle to Upper Paleolithic transition. However, radiocarbon dating on mollusk shells is often regarded as less reliable compared to bones, wood, or charcoals due to the various factors influencing their radiocarbon content (e.g., Isotope fractionation, marine reservoir effect etc.). For the development of more accurate chronologies using shells, it is fundamental to continue improving the precision of the techniques applied, as has been done for other materials (wood and bones). Thus, improving the chemical pretreatment on mollusk shells might allow researchers to obtain more reliable radiocarbon determinations allowing for the construction of new radiocarbon chronologies in archeological sites where so far it has not been possible. Furthermore, mollusk shells can provide information on the climatic and environmental variables present during their growth. Using shells for paleoclimatic reconstruction adds more evidence helpful for the interpretation of scenarios of human migration, adaptation, and behavior. Standard methods for both radiocarbon and stable isotope studies use the carbonate fraction of the shell. However, being biogenic structures, mollusk shells also consist of a minor organic fraction. The shell organic matrix has an important role in the formation of the calcium carbonate structure and is still not fully understood. This thesis explores the potential of using the shell organic matrix for radiocarbon dating and paleoenvironmental studies. The results of the work performed for this thesis represent a starting point for future research to build on, and further develop the approach and methodology proposed here.