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.     

大气湍流模糊图像的高分辨力复原算法

大气湍流是大气中的一种重要运动形式,它的存在使大气中的动量、热量、水气和污染物的垂直和水平交换作用明显增强,这种干扰作用极大地影响了光电成像系统对于目标的分辨能力。由于湍流影响而退化的图像中同时存在着幸运区域,用适当的算法可以获得高分辨力复原图像。为了获取包含幸运区域的大气湍流模糊图像,在实验室使用人造湍流,并结合短曝光技术拍摄了大气湍流干扰的序列图像。文中应用矩形交叠分块方法,改进了基于偏微分方程（PDEs）的序列图像复原算法,对获取的序列短曝光图像进行处理。结果表明,经该算法处理得到的合成图像质量有明显的提升,该算法对大气湍流造成的图像质量退化有较好的复原作用。     

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.     

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.     

Anisotropic nonlinear diffusion approach to single image resolution enhancement

In many image resolution enhancement applications, the blurring process of the imaging system is unknown. This paper discusses the problem of single image blind resolution enhancement without estimating the point spread function （PSF）. A regularization model is constructed for image enhancement based on the prior informaton of image error and image gray value,which does not need any prior in- formation of PSF. Moreover, through the solution of Euler equations, an an isotropic nonlinear diffusion equation are obtained,which can avoid the high computational cost of regularization model. Furthermore,in order to get sub-pixel superresolved image, the regularization model for image enhancement is extended to the enlargement of image, which can enlarge and enhance image at the same time. Last,to get clearer edges, a high frequency enhancement filter is used on the superresolved image. Numerical results show that the new model can get much clearer super-resolution images than traditional methods, and the peak signal to noise ratios （PSNRs） are also higher than traditional methods.     

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.     

基于PSF的太赫兹图像分辨率增强算法（英文）

近年来,太赫兹成像技术在多个领域具有广阔的应用。一套完整的太赫兹成像系统的数学模型是非常有必要的。基于点扩散函数的太赫兹图像增强模型是很好的选择。该方法将目标函数与点扩散函数进行褶积,实现了太赫兹图像的模拟传输。然后根据光学成像的过程,计算成像系统的点扩散函数。最后,基于点扩散函数对图像进行反褶积增强。该模型用于探测图像增强的结果表明,该方法有效地提高了图像的分辨率。恢复的映像包含更多细节。     

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.