Fast reconstruction of hyperspectral images from coded acquisitions using a separability assumption: erratum.

We present an erratum to our publication [Opt. Express30(5), 8174 (2022)10.1364/OE.448893] correcting a numerical value without affecting the results and conclusions of the original publication.

Fast reconstruction of hyperspectral images from coded acquisitions using a separability assumption.

We present a fast reconstruction algorithm for hyperspectral images, utilizing a small amount of data without the need for any training. The method is implemented with a dual disperser hyperspectral imager and makes use of spatial-spectral correlations by a so-called separability assumption that assumes that the image is made of regions of homogenous spectra. The reconstruction algorithm is simple and ready-to-use and does not require any prior knowledge of the scene. A simple proof-of-principle experiment is performed, demonstrating that only a small number of acquisitions are required, and the resulting compressed data-cube is reconstructed near instantaneously.

Optimized coded aperture for frugal hyperspectral image recovery using a dual-disperser system.

We present a novel acquisition scheme based on a dual-disperser architecture, which can reconstruct a hyperspectral datacube using many times fewer acquisitions than spectral bands. The reconstruction algorithm follows a quadratic regularization approach, based on the assumption that adjacent pixels in the scene share similar spectra, and, if they do not, this corresponds to an edge that is detectable on the panchromatic image. A digital micro-mirror device applies reconfigurable spectral-spatial filtering to the scene for each acquisition, and the filtering code is optimized considering the physical properties of the system. The algorithm is tested on simple multi-spectral scenes with 110 wavelength bands and is able to accurately reconstruct the hyperspectral datacube using only 10 acquisitions.

Nonlinear deconvolution of hyperspectral data with MCMC for studying the kinematics of galaxies.

Hyperspectral imaging has been an area of active research in image processing and analysis for more than 10 years, mainly for remote sensing applications. Astronomical ground-based hyperspectral imagers offer new challenges to the community, which differ from the previous ones in the nature of the observed objects, but also in the quality of the data, with a low signal-to-noise ratio and a low resolution, due to the atmospheric turbulence. In this paper, we focus on a deconvolution problem specific to hyperspectral astronomical data, to improve the study of the kinematics of galaxies. The aim is to estimate the flux, the relative velocity, and the velocity dispersion, integrated along the line-of-sight, for each spatial pixel of an observed galaxy. Thanks to the Doppler effect, this is equivalent to estimate the amplitude, center, and width of spectral emission lines, in a small spectral range, for every spatial pixel of the hyperspectral data. We consider a parametric model for the spectral lines and propose to compute the posterior mean estimators, in a Bayesian framework, using Monte Carlo Markov chain algorithms. Various estimation schemes are proposed for this nonlinear deconvolution problem, taking advantage of the linearity of the model with respect to the flux parameters. We differentiate between methods taking into account the spatial blurring of the data (deconvolution) or not (estimation). The performances of the methods are compared with classical ones, on two simulated data sets. It is shown that the proposed deconvolution method significantly improves the resolution of the estimated kinematic parameters.