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Improved blur kernel estimation with blurred and noisy image pairs
Abstract
In this paper, we propose a TV-L1 denoising model-based kernel estimation in image deblurring which uses both blurred and noisy images. More details and edges are recovered in the denoised image which is used to replace the true image and do the deconvolution. In the first instance, an initial kernel which might be very noisy can be recovered after primary kernel estimation. Whereafter, the method of hysteresis thresholding by using a mask is used to suppress the noise and finally an accurate estimated kernel can be obtained. Experimental results show that our outcome is significantly evolutional.
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We propose a regularization algorithm for color/vectorial images which is fast, easy to code and mathematically well-posed. More precisely, the regulariza- tion model is based on the dual formulation of the vectorial Total Variation (VTV) norm and it may be regarded as the vectorial extension of the dual approach de- fined by Chambolle in (13) for gray-scale/scalar images. The proposed model offers several advantages. First, it minimizes the exact VTV norm whereas standard approaches use a regularized norm. Then, the numerical scheme of minimization is straightforward to implement and finally, the number of iterations to reach the solution is low, which gives a fast regularization algorithm. Finally, and maybe more importantly, the proposed VTV minimization scheme can be easily extended to many standard applications. We apply this L 1 vectorial regularization algo- rithm to the following problems: color inverse scale space, color denoising with the chromaticity-brightness color representation, color image inpainting, color wavelet shrinkage, color image decomposition, color image deblurring, and color denoising on manifolds. Generally speaking, this VTV minimization scheme can be used in problems that required vector field (color, other feature vector) regularization while preserving discontinuities.
This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.
Deconvolution results may deviate true answers because of noise and low pass filtering. The effects of noise and blurred function to image data are compared and studied for several common deconvolution algorithms, and the maximum likelihood algorithm based on the Poisson-Markov model of super-resolution image restoration algorithms is proposed. Experiments showed that, based on the MPML algorithm proposed, it has the advantages of diminishing losses of original data in contrast to other algorithms, especially in cases involving lower noise. The recovery images display very small concussive lines and have better super-resolution recovery ability for deconvolution applications.
Tikhonov regularization approach has been accepted as one of the most effective ways to solve ill-posed problems. In the approach, the key step is the calculation of a regularization parameter. Usually, iterative methods are used to obtain the parameter. However, the obtained iterative solutions are sensitive to the initial choice of the parameter, and different initial values may lead to quite different solutions. Presently, the optimal calculation of Tikhonov regularization parameter is discussed. A method based on the Genetic Algorithm (GA) is proposed, which uses the generalized cross-validation (GCV), L-curve and Engl's error criterion as an optimal function, respectively. Numerical analysis is carried out for the load distribution model of a pin-jointed truss. It is shown that the method can achieve an optimal value of the parameter in the whole range, and therefore provides an efficient way for obtaining an optimal regularization solution.
Discretization of singular functions is an important component in many problems to which level set methods have been applied. We present two methods for constructing consistent approximations to Dirac delta measures concentrated on piecewise smooth curves or surfaces. Both methods are designed to be convenient for level set simulations and are introduced to replace the commonly used but inconsistent regularization technique that is solely based on a regularization parameter proportional to the mesh size. The first algorithm is based on a tensor product of regularized one-dimensional delta functions. It is independent of the irregularity relative to the grid. In the second method, the regularization is constructed from a one-dimensional regularization that is extended to multi-dimensions with a variable support depending on the orientation of the singularity relative to the computational grid. Convergence analysis and numerical results are given.
Soft wavelet shrinkage and total variation (TV) denoising are two frequently used techniques for denoising signals and images, while preserving their discontinuities. In this paper we show that - under spe- cific circumstances - both methods are equivalent. First we prove that 1-D Haar wavelet shrinkage on a single scale is equivalent to a single step of TV diffusion or regularisation of two-pixel pairs. Afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularisation of the Laplacian pyramid of the signal.
The total variation–based image denoising model of L. Rudin, S. Osher and E. Fatemi [Physica D 60, 259–268 (1992; Zbl 0780.49028)] has been generalized and modified in many ways in the literature; one of these modifications is to use the L 1 -norm as the fidelity term. We study the interesting consequences of this modification, especially from the point of view of geometric properties of its solutions. It turns out to have interesting new implications for data-driven scale selection and multiscale image decomposition.
Taking satisfactory photos under dim lighting conditions using a hand-held camera is challenging. If the camera is set to a long exposure time, the image is blurred due to camera shake. On the other hand, the image is dark and noisy if it is taken with a short exposure time but with a high camera gain. By combining information extracted from both blurred and noisy images, however, we show in this paper how to produce a high quality image that cannot be obtained by simply denoising the noisy image, or deblurring the blurred image alone.
Our approach is image deblurring with the help of the noisy image. First, both images are used to estimate an accurate blur kernel, which otherwise is difficult to obtain from a single blurred image. Second, and again using both images, a residual deconvolution is proposed to significantly reduce ringing artifacts inherent to image deconvolution. Third, the remaining ringing artifacts in smooth image regions are further suppressed by a gain-controlled deconvolution process. We demonstrate the effectiveness of our approach using a number of indoor and outdoor images taken by off-the-shelf hand-held cameras in poor lighting environments.
The application of the Tikhonov regularized method with constraints
- Jiao Yandong
Jiao Yandong, "The application of the Tikhonov regularized method with constraints", Hebei University of Technology, June 2004.
Restricted Landeweber iteration algorithm for image reconstruction from projection
- Li Hong-Yan
- Tong Li-Li