Study On Restoration Of Some Degraded Images

The degradation of an image is usually unavoidable during imaging, converting, trans-mitting and showing, etc. It is not expected to use degraded images in various applications. Basically, the goal of a lot of research, including image denoising, deblurring, inpainting, super-resolution and lens distortion correction, is to reconstruct an original clean image as accurately as possible from a set of maybe degraded or inadequate observations. The challenge in most inverse problems is that they are ill-posed, either the direct operator does not have an inverse, or it is nearly singular, with its inverse thus being highly noise sensitive. Consequently, it is a research hotspot and difficult problem that how to effectively solve the ill-posed inverse prob-lems and to pin down a reasonable solution. This paper makes an exploratory and innovative study of inverse problem in image processing, including image denoising, deblurring and lens distortion correction. The main contents of the paper include:(1) Image denosing methods are studied. Firstly, a novel edge-preserving image filtering method is proposed. Based on a local linear model and using the principle of Stein’s unbiased risk estimate (SURE) as an estimator for the mean squared error(MSE) from the noisy image on-ly, a simple explicit image filter is derived which can filter out noise while preserving edges and fine-scale details. Moreover, this filter has a fast and exact linear-time algorithm, whose com-putational complexity is independent of the filtering kernel size, thus it can be applied to fast image processing tasks including noise reduction, detail smoothing/enhancement, high dynam-ic range(HDR) compression. Secondly, an adaptive weighted total variation-based denoising method is proposed. This new method overcomes the limitation that total variation norm is not differentiable at zero by reducing the optimizing problem to determine the optimal affine transform coefficients in a local image patch. Finally, based on a fast approach to calculate the geodesic distance between points on a curve, a separable geodesic filtering is proposed. This method not only leads to considerable speedups over existing techniques but also can direct-ly work on color images. Further, based on the geodesic distance which is used to measure the similarity of two pixels, a simple and linear complex superpixels construction algorithm is proposed, which can generate desired superpixels are approximately uniform in size and shape.(2) Image deblurring methods are studied. Firstly, for classical image deblurring problem with known blur kernel, an effective image deblurring method is proposed, where a l0-norm regularization is minimized under the constraint that the solution explains the observations suf-ficiently well. The proposed algorithm can recover image effectively and steadily for the Gaus-sian blur and motion blur. Secondly, based on edge detection and l0-norm, a blind deconvolution method for removing motion blur from a single image is proposed. This method improves the estimation precision of blur kernel by selecting reliable edge structures and using l0-norm con-straint to preserve the sparsity of blur kernel.(3) Lens distortion correction is studied. A new simple method to determine the distortion function of camera systems suffering from radial lens distortion is proposed. Neither information about the intrinsic camera parameters nor3D-point correspondences are required. It is based on single image and uses the constraint that straight lines in the3D world project to circular arcs in the image plane under the single parameter Division Model. Differ from most of former approaches which is based on the collinearity of undistorted points, the proposed method corrects the lens radial distortion uses directly the distorted points not undistorted points, therefore it should be more robust.