A New Approaches for Image De-Blurring in Optical Imaging Application Using Derivative Compressed Sensing

The problem of reconstruction of digital images from their blurred and noisy measurements is unarguably one of the central problems in imaging sciences. Despite its ill-posed nature, this problem can often be solved in a unique and stable manner, the current presentation focuses on reconstruction of short-exposure optical images measured through atmospheric turbulence. The latter is known to give rise to random aberrations in the optical wave front, which are in turn translated into random variations of the point spread function of the optical system in use. A standard way to track such variations involves using adaptive optics. Thus, for example, the Shack–Hartmann interferometer provides measurements of the optical wave front through sensing its partial derivatives. In such a case, the accuracy of wave front reconstruction is proportional to the number of lens lets used by the interferometer and, hence, to its complexity. Accordingly, in this paper, show how to minimize the above complexity through reducing the number of the lenslets while compensating for under sampling artifacts by means of derivative compressed sensing. Additionally, it provide empirical proof that the above simplification and its associated solution scheme result in image reconstructions, whose quality is comparable to the reconstructions, obtained using conventional measurements of the optical wavefront.