Coded aperture design in mismatched compressive spectral imaging

Compressive spectral imaging (CSI) senses a scene by using two-dimensional coded projections such that the number of measurements is far less than that used in spectral scanning-type instruments. An architecture that efficiently implements CSI is the coded aperture snapshot spectral imager (CASSI). A physical limitation of the CASSI is the system resolution, which is determined by the lowest resolution element used in the detector and the coded aperture. Although the final resolution of the system is usually given by the detector, in the CASSI, for instance, the use of a low resolution coded aperture implemented using a digital micromirror device (DMD), which induces the grouping of pixels in superpixels in the detector, is decisive to the final resolution. The mismatch occurs by the differences in the pitch size of the DMD mirrors and focal plane array (FPA) pixels. A traditional solution to this mismatch consists of grouping several pixels in square features, which subutilizes the DMD and the detector resolution and, therefore, reduces the spatial and spectral resolution of the reconstructed spectral images. This paper presents a model for CASSI which admits the mismatch and permits exploiting the maximum resolution of the coding element and the FPA sensor. A super-resolution algorithm and a synthetic coded aperture are developed in order to solve the mismatch. The mathematical models are verified using a real implementation of CASSI. The results of the experiments show a significant gain in spatial and spectral imaging quality over the traditional grouping pixel technique.