M.Sc Thesis

M.Sc StudentElron Asaf Joseph
SubjectReconstruction of Hyperspectral Images from Compressive
Samples Using a Combined Spatial-Spectral Prior
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROFESSOR EMERITUS Arie Feuer
Full Thesis textFull thesis text - English Version


Hyperspectral imaging (HSI) is the capture of the electromagnetic reflectance, and in some applications fluorescence, of a scene at varying wavelengths, with relatively high spectral resolution and over a wide spectral range. This allows for different materials or substances in the scene to be distinguished from each other by using their unique reflectance or fluorescence spectra, making HSI a powerful tool. Hyperspectral imaging has many applications, ranging from earth sciences, particularly environmental studies, through biomedical research and diagnostics, to military applications.

Four important characteristics of an HSI method are spatial resolution, spectral resolution, light collection, and measurement acquisition time, with various trade-offs existing between these quantities. In recent years, there has been much work towards the decoupling of these quantities and thus the alleviation, if not elimination, of these trade-offs. To this end, it is desirable to produce a complete hyperspectral image which comprises tens of millions of numbers, one for each spatial location and spectral range, while taking far fewer measurements. Using the ideas of compressed sensing (CS), a hyperspectral image may be reconstructed from few measurements, termed “compressive samples”, through the utilization of some prior knowledge of the sensed image, i.e. it having some regularity or structure.

In our research, we address the reconstruction of a hyperspectral image from compressive samples while utilizing a combined spatial and spectral prior on the image. The spatial part of the prior assumes the image has low total variation. The spectral part of the prior is expressed using a spectral dictionary comprising the various spectra observable in the image, with the additional assumption that only a few materials participate in each pixel. This added assumption implies that there exists a sparse representation of the image using the aforementioned spectral dictionary. We define the reconstruction as an optimization problem minimizing a non-smooth functional expressing the image prior, constrained so that the hypothesis adequately explains the measurements. The measurements are assumed to have either Gaussian or Poisson statistics, where for the latter we present novel means for performing the said optimization. Numerically performing the optimization via Nesterov smoothing and an accelerated first-order optimization algorithm, we show that the suggested method allows for the reconstruction of the image with adequate fidelity, from compressive measurements simulated for synthetic as well as natural images.