Estimation of atmospheric PSF parameters for hyperspectral imaging

We present an iterative approach to solve separable nonlinear least squares problems arising in the estimation of wavelength-dependent point spread function (PSF) parameters for hyperspectral imaging. A variable projection Gauss-Newton method is used to solve the nonlinear least squares problem. An analysis shows that the Jacobian can be potentially very ill-conditioned. To deal with this ill-conditioning, we use a combination of subset selection and other regularization techniques. Experimental results related to hyperspectral PSF parameter identification and star spectrum reconstruction illustrate the effectiveness of the resulting numerical scheme. Copyright c © 2015 John Wiley & Sons, Ltd.