Lapped-windowed reconstructions in compressive spectral imaging
Date
2013
Authors
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Publisher
University of Delaware
Abstract
Traditional spectral imaging techniques scan the whole region of interest to obtain a three dimensional set that contains the spatial and spectral information of the scene. In contrast, compressive spectral imaging systems allow capturing the spatial and spectral information of the scene using two dimensional sets of random projections. These systems rely on the theory of compressed sensing (CS), which establishes that certain signals can be recovered with high probability using far fewer samples from those dictated by Nyquist. The coded aperture snapshot spectral imaging system (CASSI) is an optical imaging architecture that accomplishes compressive spectral imaging. The reconstruction of the scene is obtained by l1 norm based inverse optimization algorithms such as the gradient projections for sparse reconstruction (GPSR). The computational complexity of the inverse problem grows with order O(KN 4 L) per iteration, where N 2 and L are the spatial and spectral dimensions of the scene, respectively, and K is the number of snapshots. Many applications deal with high-dimensional spectral images, and the computational complexity becomes overwhelming since reconstructions can take up to several hours in desktop architectures. The goal of this thesis is to obtain a mathematical model for block reconstructions in CASSI, such that the reconstruction quality is not a ected and the computational complexity is reduced. The results obtained show that the lapped block reconstruction model in CASSI satis es the premises with complexity O(NB 4 L) per GPSR iteration, where B N is the block size. The proposed approach takes advantage of the structure of the transfer function of the CASSI system thus allowing the independent recovery of small lapped blocks of the measurement set. A merging process to reduce the blocking artifacts in the reconstructed scene is also described. Simulations show the bene ts of the new viii model in terms of PSNR and reconstruction time. In particular, the data cube reconstruction can be accelerated by an order of magnitude and the PSNR is improved up to 5 dB over traditional reconstruction approach.