Deblurring noisy radial-blurred images: spatially adaptive filtering approach

The deblurring of images corrupted by radial blur is studied. This type of blur appears in images acquired during any camera translation having a substantial component orthogonal to the image plane. The point spread functions (PSF) describing this blur are spatially varying. However, this blurring process does not mix together pixels lying on different radial lines, i.e. lines stemming from a unique point in the image, the so called “blur center”. Thus, in suitable polar coordinates, the blurring process is essentially a 1-D linear operator, described by the multiplication with the blurring matrix. We consider images corrupted simultaneously by radial blur and noise. The proposed deblurring algorithm is based on two separate forms of regularization of the blur inverse. First, in the polar domain, we invert the blurring matrix using the Tikhonov regularization. We then derive a particular modeling of the noise spectrum after both the regularized inversion and the forward and backward coordinate transformations. Thanks to this model, we successfully use a denoising algorithm in the Cartesian domain. We use a non-linear spatially adaptive filter, the Pointwise Shape-Adaptive DCT, in order to exploit the image structures and attenuate noise and artifacts. Experimental results demonstrate that the proposed algorithm can effectively restore radial blurred images corrupted by additive white Gaussian noise.