We report the research results of an internship carried out at SELEX Galileo, Edinburgh, facilitated by the Knowledge Transfer Network and supported by the Underpinning Defence Mathematics programme of the Ministry of Defence.
Imaging in non-visible wavelengths often requires expensive or bulky sensors, which motivates a move away from pixel sampling with many sensors towards imaging devices with fewer sensors. A novel camera design was recently proposed by a team at Rice University which employs only a single sensor or "pixel" to take an incomplete set of randomized measurements. Such a design fits naturally into the paradigm of compressed sensing, which asserts that signals with low information content can indeed be recovered from incomplete randomized sets of measurements by means of appropriate recovery algorithms.
In this project, a computer model of the compressed sensing and recovery process was built and appropriate recovery algorithms were implemented, to allow for numerical testing in order to highlight likely design issues. We describe this model in detail, and report the results of the numerical testing undertaken. Our investigation demonstrates the potential of such a technology, namely, that accurate images can be obtained while significantly reducing the number of measurements. The results also show robustness to noise and clear potential of applying such techniques to a range of contexts including multi-spectral imaging and dynamic imaging.
Written: 20 January 2011