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High-dimensional data processing: from theory to imaging applications

Periodic Reporting for period 1 - HiDDaProTImA (High-dimensional data processing: from theory to imaging applications)

Reporting period: 2016-02-01 to 2018-01-31

The research work carried out within the project HiDDaProTImA had the objective of studying fundamental limits on how information can be extracted and processed from high-dimensional data, and to design methods and algorithms able to achieve such fundamental limits. On leveraging probabilistic and deterministic mathematical frameworks to model high-dimensional data, we aimed at providing answers to the following research questions:
1. What is the minimum number of features that we need to extract from high-dimensional data in order to reliably extract information? And how to extract such information?
2. What is the advantage represented by the presence of additional side information in processing high-dimensional data? And how should we optimally capture such side information?
3. What is the optimal way to learn dictionaries to represent? What is the interplay between dictionary learning and optimizing feature extraction?
Although the answers to such research questions have an important impact on different application fields involving information processing of high-dimensional data, the focus of the work carried out within the project HiDDAProTImA has been that of imaging applications.

In this way, the results derived within the project have allowed to gauge more effectively the number of measurements and features needed to operate different tasks in imaging, as for example, video segmentation and face recognition, providing at the same time useful feature design methods.
Moreover, we have proposed a way to increase the quality of images obtained from compressive imaging devices by leveraging side information.
Finally, we have derived a mathematical framework to improve the performance of fibre bundles used for holographic endoscopy for early oesophageal cancer detection, by allowing for fast calibration and by enhancing image quality as well as discriminative power between healthy tissues and lesions.
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
The results obtained within the HiDDaProTImA project represent a progress with respect to the state-of-the-art in both theoretical and practical aspects. Namely, we have provided a novel closed-form characterisation of various fundamental limits on the number of features/measurements that need to be extracted from high-dimensional data in order to guarantee reliable classification or reconstruction.
Moreover, the techniques used to determine such mathematical characterisations have also provided explicit measurement/feature design schemes. These designs have been applied to different imaging applications, including video segmentation, face recognition, compressive hyperspectral imaging and panchromatic sharpening, providing in this way significant performance improvements with respect to state-of-the-art solutions.
These results can lead to direct socio-economic impact when considering that improved image reconstruction capacity translates into the possibility of deploying cost and time-efficient solutions for the imaging applications considered.
Moreover, the advancements carried out in the study of fibre bundles for holographic endoscopy can lead to the development of “optical biopsy” images that enable endoscopists to interrogate suspicious lesions more thoroughly without the need for complex bulky instrumentation or increased imaging examination time.
Reconstruction comparison with and without side information
Reconstruction comparison with random and designed side information measurements