Sensor networks are one of the largest data generators on the Internet. A wide range of areas corresponding to even very diverse scenarios are monitored by thousands of sensors capable of acquiring signals of various natures. Considering the usual sampling rates determined by the Shannon/Nyquist theorem, even using the usual information compression techniques, the enormous amount of information flow poses problems in the management of transmission resources, processing, and storage of the data itself.
In this scenario Compressive Sensing (CS), based on the possibility of reconstructing a signal from a few measurements, represents an emerging paradigm able to natively acquire the information directly in the non-redundant form, overcoming the limits of the sampling theorem.
Very recent studies, in part developed by the proponents of this project, have shown how hyper-complex tensor algebra, in particular quaternion algebra, represents the most natural way for the representation and processing of spatially and temporally correlated data such as those coming from arrays of audio and video sensors.
DYCOS project has the following objectives: 1) the study of a theoretical framework, and the basis for the technological development, related to CS defined in quaternion domain able to directly acquire high definition multi-dimensional signals with unique measurements; 2) the determination of a reconstruction solution, computationally parsimonious, based on end-to-end generative data-driven methods implemented with deep quaternion neural networks (DQNN) with dense or convolutional layers; 3) the implementation of a virtual testbed scenario; 4) the study and development of a theoretical/experimental framework for the performance analysis of the proposed methods.
DYCOS represents a significant improvement over the CS state of the art, greatly improving the calculation efficiency and thus extending possible application scenarios.
The innovation of the DYCOS project has the potential for a significant impact on science and technology.
The research group proposing DYCOS operates within the DIET-Sapienza laboratory Intelligent Signal Processing and MultiMedia (ISPAMM) that was founded in 2001. In this laboratory, extensive researches and studies have been carried out for many years in different fields of intelligent signal processing (ISP), with data-driven methods and linear and non-linear adaptive algorithms.
The proposed research is part of the activity that started in 2015 that has already achieved important methodological, technological, and applicative results in the quaternion ISP. These contributions are widely recognized in the international community of reference (see the above References).
To the best of our knowledge, DYCOS has different degrees of innovation in both theoretical and technological aspects related to specific areas of interest.
Considering the methodological aspects, it is necessary to deepen and extend the conditions of the compressibility of real signals to quaternion signals. The possible use of augmented statistics for non-spherical quaternion processes might lead to innovative properties that could be very useful in the compressibility of multidimensional signals. In particular, it is necessary to extend the condition of sparseness considering the quaternion algebras declined within the CS scenario, and the basis for the technological development, relative to the CS in the quaternion domain able to directly acquire high-resolution multidimensional signals with unique measurements (few projections).
To pursue this breakthrough, we have identified several topics that can be explored further in the DYCOS project. In particular, considering the research objectives (O1)-(O4) outlined above, the possible methodological and knowledge advancement contributions concerning the state of the art may concern: (i) the extension of isometric conditions to quaternion algebra; (ii) the redefinition and extension of quadratic optimization algorithms operating with under-determined L1 constraints, operating in quaternion domain; (iii) the redefinition and extension of data-driven GAN and CycleGAN methods in quaternion domain; (iv) the determination of specific application contexts and related performance analyses.
Besides, since one of the most promising areas of application for CS is IoT devices with extremely low resource constraints, the definition of thrifty methods is interesting when it can cope with hardware constraints that allow low complexity implementations.
DYCOS will reach many improvements concerning the state-of-the-art, extending CS's application scenarios and increasing computational efficiency. In order to address the above challenges, DYCOS will leverage interdisciplinary knowledge in ISPAMM.