Research work:
The research work has focused first on the analysis of fundamental limits in the classification of high-dimensional signals from linear noisy measurements, by deriving sufficient conditions on the number of measurements/features to extract from the high-dimensional data to guarantee reliable classification, for both cases of random and design measurements.
Subsequently, research work has been devoted to the analysis of the impact of side information in classification and regression tasks. We first considered the case of random measurements and then moved to the study of how to optimally capture side information to aid reconstruction.
A further line of research has focused on the use of deep neural networks as a way to learn effective data representations for imaging applications as magnetic resonance imaging (MRI), computed tomography (CT) and scanning transmission electron microscopy (STEM). Our aim has been to develop a mathematical framework that would allow an analysis of the interaction between network architecture, training data, measurement schemes and image structure in determining reconstruction performance of deep neural networks.
Further research work developed in collaboration with the Centre for Advanced Photonics and Electronics (CAPE) and the Centre for Mathematical Imaging in Healthcare (CMIH) of University of Cambridge has focused on the problem of early oesophageal cancer detection with holographic endoscopy. We have developed a mathematical framework that allows to increase computational efficiency of fibre calibration as well as image reconstruction quality.
Exploitation and dissemination of the results:
Results regarding classification of high-dimensional data have been shown useful in predicting performance of video motion segmentation and face recognition applications. These contents have been included in a journal published in the IEEE Transactions of Signal Processing.
The study of classification of high-dimensional data has also found another important application in the field of biomedical signal processing. Namely, in collaboration with researchers from the Department of Computer Science of University of Porto, Portugal, we have developed a novel algorithm for heart sound signal segmentation. This work has been presented at the IEEE Computing in Cardiology Conference.
The results on the impact of side information in processing high-dimensional data have been applied to two hyperspectral imaging applications. We have considered first a compressive hyperspectral imaging problem, where hyperspectral images of a subject are recovered from the compressive measurements. In this case, side information is represented by a simple RGB image of the same subject, and its presence is shown to improve significantly reconstruction performance (Fig. 1). Then, we have tested the impact of side information measurement designs in a pan-sharpening application, which involves the recovery of a high-resolution colour image from a high-resolution pan-chromatic snapshot and low-resolution hyperspectral images of the same scene. We have then observed that careful design of the compressive hyperspectral measurements improved the image reconstruction quality with respect to random measurements (Fig. 2). The results obtained in the study of side information have been disseminated via a journal publication in the IEEE Transactions on Information Theory and a submission to the IEEE Transaction on Signal Processing.
Finally, we have considered a holographic endoscopy application for early oesophageal cancer detection, in collaboration with the Centre for Advanced Photonics and Electronics (CAPE) and the Centre for Mathematical Imaging in Healthcare (CMIH) of University of Cambridge. The proposed reconstruction approach has been tested on experimental equipment with both synthetic holographic images as well as images of healthy and lesion samples extracted from oesophageal tissue of small laboratory animals (mic
