Image Deblur in Gradient Domain

This paper proposes a new method for natural-image deblur based on a single blurred image. The natural image prior, a sparse gradient distribution, is enforced using a gradient histogram remapping method in the proposed deblur algorithm. The proposed objective function for blind deconvolution is solved by an alternating minimization method. The point spread function and the unblurred image are updated alternately. The proposed method is able to produce high-quality deblurred results with low computational costs. Both synthetic and real blurred images are tested in the experiments. Encouraging experimental results show that the newly proposed method could effectively restore images blurred by complex motion

A proximal iteration for deconvolving Poisson noisy images using sparse representations

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are: First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a {\it non-linear} degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a non-smooth sparsity-promoting penalties over the image representation coefficients (e.g. $\ell_1$-norm). Third, a fast iterative backward-forward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy