M.Sc Thesis

M.Sc StudentPfeffer Yehuda
SubjectCompressive Sensing for Hyperspectral Imaging
DepartmentDepartment of Electrical and Computers Engineering
Supervisors DR. Michael Zibulevsky
PROF. Ehud Rivlin
Full Thesis textFull thesis text - English Version


Compressive Sensing (CS) is an emerging field of generalized sampling that is based on the understanding that for certain types of signals, it is possible and practical to sample only a fraction of the minimal number of samples required by the Nyquist theorem. If the signal is sparse, then CS theory asserts that it can be reconstructed from its samples by means of non-linear optimization.

We introduce a system for hyperspectral imaging, which includes a micro-mirror array that projects subsets of image pixels onto a prism (or diffraction grating), followed by a CCD-type sensor. This system allows generalized sampling schemes including Compressed Sensing. We acquire only a fraction of the samples that are required to obtain the full-resolution signal (hyperspectral cube in our case), and by means of non-linear optimization recover the underlying signal. We use a prior knowledge about the signal sparsity in some fixed dictionary, and also its limited total variation. In the practical setting developed here, the feasible sampling is not ideal for CS due to practical limitations, and the sensed signal does not necessarily meet the strict sparsity demands of CS theory. Therefore we introduce additional measurements of full-resolution image using small number of filters similar to RGB. As a result, we obtain a feasible system for hyperspectral imaging that enables faster acquisition compared to traditional sampling systems.

We dedicated one chapter for theoretical analysis of different noises typical to hyperspectral imaging, and the relation between noise in the acquisition process and the error in the final reconstruction result. The results were verified by simulations.