A cross-validation framework for solving image restoration problems

The restoration problem deals with images in which information has been destroyed or obscured. In this paper, we present a framework for addressing image restoration problems in which the goal is to recover information about the image. Restoration algorithms often use tentative assumptions to compensate for the information lost in the degradation process. We propose cross-validation as a method for testing such assumptions. Viewed in this way, cross-validation is capable of addressing a number of key image restoration problems. We discuss the various options available for defining and evaluating the cross-validation criterion. Furthermore, we survey recent developments concerning cross-validation in image restoration and demonstrate the power of cross-validation in addressing several image restoration problems—regularization parameter estimation, blur identification, constraint assessment, and an optimal stopping rule for iterative restoration.     

Multiple resolution image restoration

A new algorithm for solving the deconvolution problem is proposed. This algorithm uses the wavelet transform to induce a multiresolution approach to deconvolve a blurred signal/image. The low resolution part of a signal/image is restored first and then high resolution information is added successively into the estimation process. Two different ways to incorporate the image space positivity constraint, namely loosely and strictly, are discussed. In to most restoration algorithms, the positivity constraint is applied directly in the transformed domain. The performance of the algorithm in the presence of noise is also investigated     

Wavelet domain image resolution enhancement

A wavelet-domain image resolution enhancement algorithm which is based on the estimation of detail wavelet coefficients at high resolution scales is proposed. The method exploits wavelet coefficient correlation in a local neighbourhood sense and employs linear least-squares regression to estimate the unknown detail coefficients. Results show that the proposed method is considerably superior to conventional image interpolation techniques, both in objective and subjective terms, while it also compares favourably with competing methods operating in the wavelet domain.     

Efficient Huber-Markov edge-preserving image restoration.

The regularization of the least-squares criterion is an effective approach in image restoration to reduce noise amplification. To avoid the smoothing of edges, edge-preserving regularization using a Gaussian Markov random field (GMRF) model is often used to allow realistic edge modeling and provide stable maximum a posteriori (MAP) solutions. However, this approach is computationally demanding because the introduction of a non-Gaussian image prior makes the restoration problem shift-variant. In this case, a direct solution using fast Fourier transforms (FFTs) is not possible, even when the blurring is shift-invariant. We consider a class of edge-preserving GMRF functions that are convex and have nonquadratic regions that impose less smoothing on edges. We propose a decomposition-enabled edge-preserving image restoration algorithm for maximizing the likelihood function. By decomposing the problem into two subproblems, with one shift-invariant and the other shift-variant, our algorithm exploits the sparsity of edges to define an FFT-based iteration that requires few iterations and is guaranteed to converge to the MAP estimate.     

基于图像增强和复原的图像去雾方法研究

雾霭等天气下获得的图像存在对比度低、颜色退化、景物模糊等一系列图像退化的问题,直接影响了对图像信息的有效利用。因此,对雾天图像进行有效的去雾处理,有效改善降质图像的质量,具有一定的实际意义。分析讨论基于图像增强的多尺度Retinex算法和利用图像复原原理的基于暗原色先验理论的去雾算法,并对具有不同特点的单幅有雾图像进行去雾仿真。实验结果表明,不同理论基础的两种去雾算法各有特点,基于暗原色理论处理得到的图像去雾效果更显著,算法运行速度更快。     

Hessian-based norm regularization for image restoration with biomedical applications

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, i.e., convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iteratively reweighted least-square type and results from a majorization-minimization approach. It relies on a problem-specific preconditioned conjugate gradient method, which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.     

Wavelet domain image resolution enhancement using cycle-spinning

A wavelet domain image resolution enhancement method is proposed. The method adopts the cycle-spinning methodology adapted for use in the wavelet domain. The perceptual and objective quality of resolution enhanced images compare favourably with recently emerged algorithms in the field     

Polyphase back-projection filtering for image resolution enhancement

The method for reconstruction and restoration of super-resolution images from sets of low-resolution images presented is an extension of the algorithm proposed by Irani and Peleg (1991). After estimating the projective transformation parameters between the image sequence frames, the observed data are transformed into a sequence with only quantised sub-pixel translations. The super-resolution reconstruction is an iterative process, in which a high-resolution image is initialised and iteratively improved. The improvement is achieved by back-projecting the errors between the translated low-resolution images and the respective images obtained by simulating the imaging system. The imaging system's point-spread function (PSF) and the back-projection function are first estimated with a resolution higher than that of the super-resolution image. The two functions are then decimated so that two banks of polyphase filters are obtained. The use of the polyphase filters allows exploitation of the input data without any smoothing and/or interpolation operations. The presented experimental results show that the resolution improvement is better than the results obtained with Irani and Peleg's algorithm.     

Adapting total generalized variation for blind image restoration

Multidimensional Systems and Signal Processing - In this paper, a fast blind deconvolution approach is proposed for image deblurring by modifying a recent well-known natural image model, i.e., the...     

Two iterative image restoration algorithms with applications to nuclear medicine

Two methods for recovering an image that has been degraded while being processed are presented. The restoration problem is formulated as a constrained optimization problem in which a measure of smoothness based on the second derivatives of the restored image is maximized subject to the constraint that noise energy is equal to the energy in the difference between the distorted and blurred images. The approach is based on the Lagrange multiplier method. The first algorithm reduces the problem to the computation of few discrete Fourier transforms and allows control of the degree of sharpness and smoothness of the restored image. The second algorithm with weight matrices included allows the handling of edges and flat regions in the image in a pleasing manner for the human visual system. In this case the iterative conjugate gradient method is used in conjunction with the discrete Fourier transform to minimize the Lagrangian function. The application of these algorithms to nuclear medicine images is presented.     

Phase-driven spatially variant regularization for image resolution enhancement

A phase-driven spatially variant regularization approach is proposed in this letter to perform image resolution enhancement. The proposed approach adaptively adjusts the degree of regularization using the phase coherence measure of the local content of the image. This is in contrast to that a spatially invariant regularization parameter is exploited for the whole image in conventional approaches. Experiments are conducted to demonstrate the superior performance of the proposed approach.     

ℒ-M-S filters for image restoration applications

A new filtering architecture is proposed, generalizing some previously introduced multilevel median filters. An efficient design procedure for the new filtering architecture is demonstrated for image restoration application. Simulation results show a good noise rejection performance, combined with a fine detail preservation capability.     

Efficient blind image restoration using discrete periodic Radon transform

Restoring an image from its convolution with an unknown blur function is a well-known ill-posed problem in image processing. Many approaches have been proposed to solve the problem and they have shown to have good performance in identifying the blur function and restoring the original image. However, in actual implementation, various problems incurred due to the large data size and long computational time of these approaches are undesirable even with the current computing machines. In this paper, an efficient algorithm is proposed for blind image restoration based on the discrete periodic Radon transform (DPRT). With DPRT, the original two-dimensional blind image restoration problem is converted into one-dimensional ones, which greatly reduces the memory size and computational time required. Experimental results show that the resulting approach is faster in almost an order of magnitude as compared with the traditional approach, while the quality of the restored image is similar.     

Integrated recurrent neural network for image resolution enhancement from multiple image frames

The paper presents a new method for image resolution enhancement from multiple image frames using an integrated recurrent neural network (IRNN). The IRNN is a set of feedforward neural networks working collectively with the ability of having feedback of information from its output to its input. As such, it is capable of both learning and searching the optimal solution in the solution space for optimisation problems. In other words, it combines the advantages of both the Hopfield network and the multilayered feedforward network in solving the enhanced image reconstruction problem. Simulation results demonstrate that the proposed IRNN can successfully be used to enhance image resolution. The proposed neural network based method is promising for real-time applications, especially when the inherent parallelism of computation of the neural network is explored. Further, it can adapt itself to the various conditions of the reconstruction problem by learning     

A statistical image resolution enhancement approach for mixed-resolution video

Many scalable video compression techniques utilise a mixed-resolution scheme, which down-samples some frames at the encoder to produce reduced-resolution frames while keeping resolutions of other frames unchanged as full resolutions, in order to achieve higher compression gain. Image enlargement technique is required at the decoder to recover the original full-resolution frames for this mixed-resolution video system set-up. This article proposes a Bayesian approach to enlarge the reduced-resolution frame via its maximum a-posterior estimation, using the information from the observed reduced-resolution frame, plus more detailed information extracted from available neighbouring frames in full resolution. Experiments are conducted to justify that the proposed approach outperforms a few conventional approaches.     

Dual regularization-based image resolution enhancement for asymmetric stereoscopic images

Asymmetric stereoscopic imaging technique utilizes a pair of lower-resolution and full-resolution images to reduce the data storage requirement of stereoscopic images and videos, while maintaining fairly good quality in 3D perception. This paper proposes a resolution enhancement approach to reconstruct the original full-resolution image for this asymmetric stereoscopic system setup. The proposed approach exploits a dual regularization scheme: (i) a saliency-based regularization function is proposed to adaptively adjust the degree of regularization based on the local content of the image; and (ii) an occlusion-sensitive regularization function is proposed to exploit the correlation between the observed lower-resolution image and the observed full-resolution image in the neighboring view. Experiments are conducted to justify that the proposed approach outperforms a few conventional approaches.     

面向图像复原的广义岭估计模式法波前重构

为了提高自适应光学图像的复原效果,提出了一种面向图像复原的广义岭估计Zernike模式波前重构算法。首先,按照用时间换精度的思路,把广义岭估计引入自适应光学波前重构算法中。改善最小二乘估计的奇异性,抑制波前测量误差的放大。然后,引入迭代计算提高方程的解算精度,进一步提高点扩散函数(PSF)重建质量。最后,利用广义岭估计重建的PSF对降质图像进行复原实验验证PSF的重建质量。实验结果证明,广义岭估计PSF的复原效果比最小二乘估计PSF高约15%,更接近成像系统的光学衍射极,同时复原计算迭代次数也减少了35%。新算法重构的PSF在图像复原中有更好的图像重建效果。     

Adaptive image restoration using a generalized Gaussian model forunknown noise

A model adaptive method is proposed for restoring blurred and noise corrupted images. The generalized p-Gaussian family of probability density functions is used as the approximating parametric noise model. Distribution shape parameters are estimated from the image, and the resulting maximum likelihood optimization problem is solved. An iterative algorithm for data-directed restoration is presented and analyzed.     

Piecewise and local image models for regularized image restorationusing cross-validation

We describe two broad classes of useful and physically meaningful image models that can be used to construct novel smoothing constraints for use in the regularized image restoration problem. The two classes, termed piecewise image models (PIMs) and focal image models (LIMs), respectively, capture unique image properties that can be adapted to the image and that reflect structurally significant surface characteristics. Members of the PIM and LIM classes are easily formed into regularization operators that replace differential-type constraints. We also develop an adaptive strategy for selecting the best PIM or LIM for a given problem (from among the defined class), and we explain the construction of the corresponding regularization operators. Considerable attention is also given to determining the regularization parameter via a cross-validation technique, and also to the selection of an optimization strategy for solving the problem. Several results are provided that illustrate the processes of model selection, parameter selection, and image restoration. The overall approach provides a new viewpoint on the restoration problem through the use of new image models that capture salient image features that are not well represented through traditional approaches.