A Fast non-Iterative Algorithm for the Removal of Blur Caused by Uniform Linear motion in X-Ray Images

The paper discusses a new technique for the removal of blur in a X-ray caused by uniform linear motion. This method assumes that the linear motion corresponds to an integral number of pixels and is aligned with the horizontal (or vertical) sampling. The proposed approach can be summarized as follows: Given is a gray value vector g, the row of the digitized degraded X-ray . The unknown to be recovered is f, the corresponding restored row of the . The relation between these two components is H.f = g, which will be used as constraint. The matrix H is known or it can be estimated from the degraded using its Fourier spectrum. The vector g is of N entries, while the vector f is of M=N+n-1 entries ( M>N), where n is the length of the blurring process in pixels. The problem consists of solving this underdetermined system H.f = g. However, since there is an infinite number of exact solutions for f that satisfy H.f = g, an additional criterion that finds a sharp restored is required. The paper contribution lies in using a new criterion for restoration a blurred : the solution is defined as the vector in the solution space of the underdetermined system whose first N components has the minimum distance to the measured data, i.e. , where are the first N elements of f . A fast non-iterative algorithm of solving the underdetermined linear system under the mentioned constraint is proposed. The procedure is repeated for each row of the degraded . The quality of restoration is as satisfactory as the classic methods, nevertheless the computation load is decreased considerably. The proposed method have been tested on several Xray s with simulated blur degradation.