KRISM—Krylov Subspace-based Optical Computing of Hyperspectral Images

Abstract

Relative intensity Wavelength (nm) KRISM Spectrometer spatial code measured spectrum S-polarized light polarizing beam splitter LCoS SLM diffraction grating P-polarization S-polarization operator #1. spatially-coded spectrum measurement spectral code measured spatial image P-polarized light operator #2. spectrally-coded spatial measurement 1 1 Fig. 1.Hyperspectral imagers resolve scenes at high spatial and spectral resolutions. We propose a novel architecture called KRISM that provides the ability to implement two operators: a spatially-coded spectrometer and a spectrally-coded spatial imager. By iterating between the two, we can acquire a low rank approximation of the hyperspectral image in a light efficient manner with very few measurements. The left image shows optical schematics for implementing the two operators. On the right, we show a hyperspectral image of a scene illuminated with a compact fluorescent lamp (CFL) acquired using our lab prototype. The proposed method enables high spatial and spectral resolution as observed in the zoomed-in image patches and CFL peaks, respectively.We present an adaptive imaging technique that optically computes a lowrank approximation of a scene's hyperspectral image, conceptualized as a matrix. Central to the proposed technique is the optical implementation of two measurement operators: a spectrally-coded imager and a spatially-coded spectrometer. By iterating between the two operators, we show that the top singular vectors and singular values of a hyperspectral image can be adaptively and optically computed with only a few iterations. We present an optical design that uses pupil plane coding for implementing the two operations and show several compelling results using a lab prototype to demonstrate the effectiveness of the proposed hyperspectral imager.

On Space-spectrum Uncertainty Analysis for Coded Aperture Systems

“…This result was first explored in [7] and [9] where they stated that a slit trades off spatial and spectral resolution. Our paper builds on their results by providing a concise expression for the tradeoff.…”

“…Hyperspectral imagers. Apart from programmable spectral filtering, several hyperspectral imaging architectures [8][9][10] rely on obtaining spectrally-modulated images. Our findings have a direct implication on such setups, as a key requirement of such setups is to capture high resolution images without sacrificing spectral resolution.…”

“…The analysis in this paper is for the optical setup shown in Fig. 1, commonly used in prior art for spectral filtering [4,[7][8][9]. The optical system consists of a series of lenses of focal length f , each subsequent pair separated by 2 f .…”

Hyperspectral Image Super-Resolution Based on Spatial Group Sparsity Regularization Unmixing

“…Some Matrix factorization-based methods considering the spectral basis and spatial structures have been proposed; for example, Chen et al [27] proposed a joint spatial-spectral resolution method with spectral matrix factorization and spatial sparsity constraints. The property that real-world HSI are locally low-rank is used to partition the hyperspectral image into patches and helps the optical computing of HSIs [28].…”

Image-based acquisition and modeling of polarimetric reflectance

“…Existing datasets mainly focus on the scalar or RGB intensity of scattered light, neglecting other physical properties of light such as its spectrum and polarization state [Baek et al 2018;Kadambi et al 2015;Saragadam and Sankaranarayanan 2019]. While neither is strictly necessary to produce images that are meant for human consumption, they are play an important role in applications that require a particularly high level of accuracy, such as predictive rendering.…”