Fast and Accurate Multiplicative Decomposition for Fringe Removal in Interferometric Images
Abstract: Airborne hyperspectral images can be efficiently obtained with imaging static Fourier transform spectrometers. However, to be effective on any location, this technology requires to know the relief of the scene. This is not a straightforward process, as the horizontal interferen interference ce fringes on the images, which are necessary for spectrum construction, prevent efficient stereoscopic processing. We present a novel variational model for multiplicative image decomposition to separate the fringes from the panchromatic image of the scene scene.. This multiplicative model is much more physically accurate than previous additive decomposition models inspired by cartoon-texture texture decomposition. It combines fully smoothed total variation operators and one one-dimensional (1-D) D) Fourier transform. Smoothed total t variation is adopted to avoid staircasing artifacts caused by traditional total variation regularization. The use of a 11-D D Fourier transform is suggested by the geometry of the fringes, in order to circumvent the lack of horizontal periodicity in the interferometric pattern. We also present an optimization algorithm. Finally, a second algorithm is introduced, whose convergence is not mathematically guaranteed. However, it systematically approaches the solution of the first one in much less computation time. Our experimental evaluation on real and simulated images shows that the proposed model separates fringes from the panchromatic