Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers Ashwin A. Wagadarikar a , Nikos P. Pitsianis abc , Xiaobai Sun b , David J. Brady a a Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708 b Department of Computer Science, Duke University, Durham, NC 27708, USA c Department of Electrical and Computer Engineering, Aristotle University, Thessaloniki, 54124, Greece ABSTRACT This paper describes numerical estimation techniques for coded aperture snapshot spectral imagers (CASSI). In a snapshot, a CASSI captures a two-dimensional (2D) array of measurements that is an encoded representation of both spectral information and 2D spatial information of a scene. The spatial information is modulated by a coded aperture and the spectral information is modulated by a dispersive element. The estimation process decodes the 2D measurements to render a three-dimensional spatio-spectral estimate of the scene, and is therefore an indispensable component of the spectral imager. Numerical estimation results are presented. Keyword list: coded aperture snapshot spectral imager, system modeling, spectral image estimation 1. INTRODUCTION A spectral imager captures the power spectral density of light as a function of wavelength λ and spatial location (x, y). In other words, it acquires a three-dimensional (3D) data cube of information, (x, y; λ), about the scene being imaged. Knowledge of the spectral content at various spatial locations can be valuable in identifying the composition and structure of objects in the scene being observed by the spectral imager. It is common and conventional for most spectral imagers to acquire such a spatio-spectral data cube through temporal scanning either spectrally or spatially. 1–3 While temporal scanning is suitable for spectral imaging of a static scene, it complicates and limits the subsequent image processing and analysis for a dynamic scene due to the artifacts induced by the temporal overlap of the scanning operation of the spectral imager with dynamic changes in the scene. In contrast, a snapshot spectral imager eliminates such temporal overlap. In Coded Aperture Snapshot Spectral Imagers (CASSI), 4, 5 the 3D spatio-spectral information about a scene of interest is first encoded and acquired with one snapshot at the two-dimensional (2D) detector array. An estimate of the 3D data cube is then obtained by decoding the 2D array of measurements with numerical estimation techniques. In encoding the 3D information into a 2D representation, a CASSI system utilizes a coded aperture and one or more dispersive elements to modulate the optical field from a scene. Here, we are particularly interested in the single disperser CASSI (SD-CASSI). 4 It uses an objective lens to image the scene on to the aperture of a coded aperture spectrometer. 6 In essence, the SD-CASSI extends the utility of the coded aperture spectrometer to coded aperture spectral imaging. In decoding, the gradient projection for sparse reconstruction (GPSR) method was used in previous work to estimate the data cube, based on the assumption that the data cube had a sparse representation in a wavelet basis. 4 In this paper, we report on alternative methods for estimating the spatio-spectral information from a 2D snapshot SD-CASSI detector measurement. The rest of the paper is organized as follows. In the next section, we describe a particular SD-CASSI prototype, and the discretization of a simple mathematical model for light propagation through the instrument. In Section 3, we describe the process of calibrating SD-CASSI in order to provide image estimation algorithms with a system-specific model that also accounts for additional factors that are absent in the simplified light propogation model. In Section 4, we describe three spectral image estimation algorithms. In Section 5, we present our comments on experimental results generated by the use of the estimation algorithms on experimental data. Section 6 concludes the paper. Send correspondence to David J. Brady: dbrady@duke.edu Invited Paper Image Reconstruction from Incomplete Data V, edited by Philip J. Bones, Michael A. Fiddy, Rick P. Millane, Proc. of SPIE Vol. 7076, 707602, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.795545 Proc. of SPIE Vol. 7076 707602-1