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This paper proposes a new method that solves the problem of inverse synthetic aperture radar image cross-range scaling by estimating the rotational velocity (RV) using the expansion–rotation–scale relationship between two range–Doppler (RD) images. This method is composed of three steps. The first step is preprocessing to construct 2-D Fourier transform images and initial polar-mapped images. In this step, two RD images are 2-D Fourier transformed to avoid the necessity of finding the rotation center; then, the transformed images are polar mapped with identical polar grids to convert rotation into translation in the \theta-direction only. The second step is a coarse search that finds the angular shift that provides the maximum correlation between two polar images. The angular shift found is used as the initial relative rotation angle (RA), and the initial relative scaling factor (RSF) is calculated using the RV which is equal to the angular shift divided by the time delay between the images. The third step is the optimization of the relative RA using the Nelder–Mead approach, with the RSF updated using the relative RA derived during each iteration. In simulations using a Mig-25 aircraft, composed of ideal point scatterers, and the measured data from a Boeing 747-400, the targets were properly rescaled in the range–cross-range domain due to the accurate estimation of the RV. [ABSTRACT FROM AUTHOR]

The linear mixture model is a convenient way to describe image pixels as a linear combination of pure spectra – termed endmembers. The fractional contribution from each endmember is calculated through inversion of the linear model. Despite the simplicity of the model, a nonnegativity constraint that is imposed on the fractions leads to an unmixing problem for which it is hard to find a closed analytical solution. Current solutions to this problem involve iterative algorithms, which are computationally intensive and not appropriate for unmixing large number of pixels. This paper presents an algorithm to build fuzzy membership functions that are equivalent to the least square solution of the fully constrained linear spectral unmixing problem. The efficiency and effectiveness of the proposed solution is demonstrated using both simulated and real data. [ABSTRACT FROM AUTHOR]