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.

Uncovering the encoding and transmission of behaviourally relevant information in neural activity

Most cognitive functions require the encoding and routing of information across distributed networks of brain regions. Information propagation is typically attributed to physical connections existing between brain regions, and contributes to the formation of spatially correlated activity patterns, known as functional connectivity. While structural connectivity provides the anatomical foundation for neural interactions, the exact manner in which it shapes functional connectivity is complex and not yet fully understood. Additionally, traditional measures of directed functional connectivity only capture the overall correlation between neural activity, and provide no insight on the content of transmitted information, limiting their ability in understanding neural computations underlying the distributed processing of behaviorally-relevant variables. In this work, we first study the relationship between structural and functional connectivity in simulated recurrent spiking neural networks with spike timing dependent plasticity. We use established measures of time-lagged correlation and overall information propagation to infer the temporal evolution of synaptic weights, showing that measures of dynamic functional connectivity can be used to reliably reconstruct the evolution of structural properties of the network. Then, we extend current methods of directed causal communication between brain areas, by deriving an information-theoretic measure of Feature-specific Information Transfer (FIT) quantifying the amount, content and direction of information flow. We test FIT on simulated data, showing its key properties and advantages over traditional measures of overall propagated information. We show applications of FIT to several neural datasets obtained with different recording methods (magneto and electro-encephalography, spiking activity, local field potentials) during various cognitive functions, ranging from sensory perception to decision making and motor learning. Overall, these analyses demonstrate the ability of FIT to advance the investigation of communication between brain regions, uncovering the previously unaddressed content of directed information flow.