Computed Tomography Imaging Spectrometer simulator

This repository details a computed tomography imaging spectrometer (CTIS) simulator, which is designed to simulate the generation of a center zeroth-order and surrounding first-order diffraction spots of a diffractive optical element (DOE).

Overview and use

The CTIS simulator is explained in the supplementary material of our paper The hybrid approach - Convolutional Neural Networks and Expectation Maximization Algorithm - for Tomographic Reconstruction of Hyperspectral Images [1].

This repository contains the following MATLAB scripts

• em.m: Expectation Maximization (EM) algorithm (see function for details, inputs and output)
• generateH.m: Generate a system matrix $\boldsymbol{H}$ for a computed tomography imaging spectrometer (see function for details, inputs and output)
• demo.m: Demonstration file showing generation of system matrix $\boldsymbol{H}$, simulation of CTIS image $g$ and reconstruction of hyperspectral cube $f$ using the EM algorithm.

and .mat files:

• cubeHSIcolorchecker.mat: A $400\times200\times216$ hyperspectral cube captured by our pushbroom hyperspectral imaging system.
• halogen25_mat: $1\times 25$ column vector containing the spectrum of the halogen lamps used as illumination for the wavelength range 400 nm to 740 nm.
• wavelength25_mat: $1\times 25$ column vector containing the wavelength axis for 25 spectral bands (400 nm to 740 nm)
• sensitivity25.mat: $9 \times 25$ matrix containing the diffraction sensitivity (diffraction efficiency of the DOE, transmission of optical system and sensor response) for the 9 diffraction order spots.

Brief introduction to CTIS

A CTIS system is described by the linear imaging equation: $$\boldsymbol{g} = \boldsymbol{H}\boldsymbol{f}+ \boldsymbol{n},$$

where $\boldsymbol{g}$ is a column vector with $q^2$ elements and $f$ is the vectorized hyperspectral cube with $r = x \cdot y \cdot z$ voxels, where $x$, $y$ and $z$ denote the two spatial dimensions and the number of spectral channels, respectively, while $n$ corresponds to a random noise vector. The $q^2 \times r$ system matrix $H$ describes the projection of the $i$-th voxel in $f$ to the $j$-th pixels in $g$ - equivalent to the nine projections shown below, which consist of a central zeroth order, surrounded by eight first orders.

References

M.J. Ahlebæk, M.S. Peters, W.-C. Huang, M.T. Frandsen, R.L. Eriksen and B. Jørgensen, “The hybrid approach — convolutional neural networks and expectation maximisation algorithm — for tomographic reconstruction of hyperspectral images”, J. Spectral Imaging 12, a1 (2023), DOI: 10.1255/jsi.2023.a1