Spatio-spectral deconvolution for high resolution spectral imaging with an application to the estimation of sun-induced fluorescence

We propose a signal deconvolution procedure for imaging spectrometer data, where a measured point spread function (PSF) is deconvolved itself before being used for deconvolution of the signal. We evaluate the effectiveness of our procedure for improvement of the spatio-spectral signal, as well as our target application, i.e. estimation of sun-induced fluorescence (SIF). Imaging spectrometers are well established instruments for remote sensing. When used for scientific purposes these instruments are usually calibrated on a regular basis. In our case the point spread function of the optics is measured in an elaborate procedure with a tunable monochromator point light source. PSFs are measured at different pixel positions of the imaging sensor, i.e. at different spatio-spectral locations, and averaged in order to get an as accurate PSF as possible. We investigate error sources in this calibration process by simulating the procedure in silico. Averaging as well as the spectral and spatial width of the point source introduce some smoothness in the measured PSF. We propose corrective measures, i.e. deconvolution of the PSF itself and median instead of mean averaging, leading to a set of sharper PSFs. We test the performance of these PSFs in deconvolving simulated as well as real hyperspectral images. For deconvolution we test a set of well-known, off the shelf deconvolution algorithms. Quantitatively in terms of PSNR (Peak Signal to Noise Ratio) a combination of Wiener filtering and sharpened PSFs yields strongest improvements, while using Wiener filtering with non-sharpened PSFs even deteriorates the signal. Comparing deconvolution results of the simulated data with results of real data reveals, that visually very similar effects can be observed. This well supports the assumption, that our findings are also valid for real spatio-spectral data. Surprisingly, the choice of PSF, sharpened or not, is of little effect for SIF estimation with the iFLD algorithm in the O2A band. Quantitatively we find that deconvolution reduces the overall error of SIF by a factor of 3.8, when using Wiener filtering instead of the currently used 1 iteration of vanCittert's method. For SIF estimation in the O2B band we observe a totally different behavior, where all deconvolution methods yield unreliable results with mostly well above 200% relative error and high standard deviations. In the discussion we can only speculate on possible reasons for this unreliability. As conclusion we therefore propose to use the O2A band for SIF estimation together with classic Wiener filtering for deconvolution of spatio-spectral data.