Blind image restoration by anisotropic regularization

This paper presents anisotropic regularization techniques to exploit the piecewise smoothness of the image and the point spread function (PSF) in order to mitigate the severe lack of information encountered in blind restoration of shift-invariantly and shift-variantly blurred images. The new techniques, which are derived from anisotropic diffusion, adapt both the degree and direction of regularization to the spatial activities and orientations of the image and the PSF. This matches the piecewise smoothness of the image and the PSF which may be characterized by sharp transitions in magnitude and by the anisotropic nature of these transitions. For shift-variantly blurred images whose underlying PSFs may differ from one pixel to another, we parameterize the PSF and then apply the anisotropic regularization techniques. This is demonstrated for linear motion blur and out-of-focus blur. Alternating minimization is used to reduce the computational load and algorithmic complexity.     

A multiplicative iterative algorithm for box-constrained penalized likelihood image restoration

Image restoration is a computationally intensive problem as a large number of pixel values have to be determined. Since the pixel values of digital images can attain only a finite number of values (e.g., 8-bit images can have only 256 gray levels), one would like to recover an image within some dynamic range. This leads to the imposition of box constraints on the pixel values. The traditional gradient projection methods for constrained optimization can be used to impose box constraints, but they may suffer from either slow convergence or repeated searching for active sets in each iteration. In this paper, we develop a new box-constrained multiplicative iterative (BCMI) algorithm for box-constrained image restoration. The BCMI algorithm just requires pixelwise updates in each iteration, and there is no need to invert any matrices. We give the convergence proof of this algorithm and apply it to total variation image restoration problems, where the observed blurry images contain Poisson, Gaussian, or salt-and-pepper noises.     

最大似然空间变化图像恢复算法

在光学图像处理中,把光学成像系统看做线性空间变化系统具有普遍意义。从实际光学系统成像过程出发,考虑光学系统的点扩散函数的空间变化特性和探测器噪声特性,建立了空间变化成像模型。在此成像模型基础上,基于最大似然法提出了空间变化的Richardson-Lucy(SVRL)图像恢复算法。为了分析SVRL算法的性能,实验中利用ZEMAX软件计算不同视场的点扩散函数,而后利用此空间变化点扩散函数进行成像仿真,得到仿真成像结果,最后分别采用0视场、0.5视场、0.7视场、1视场的点扩散函数以及空间变化点扩散函数对仿真图像进行恢复。实验结果表明,对于实际的空间变化光学系统,SVRL算法的图像恢复效果十分有效。     

Local noise weighted filtering for emphysema scoring of low-dose CT images

Computed tomography (CT) has become the new reference standard for quantification of emphysema. The most popular measure of emphysema derived from CT is the pixel index (PI), which expresses the fraction of the lung volume with abnormally low intensity values. As PI is calculated from a single, fixed threshold on intensity, this measure is strongly influenced by noise. This effect shows up clearly when comparing the PI score of a high-dose scan to the PI score of a low-dose (i.e., noisy) scan of the same subject. In this paper, the noise variance (NOVA) filter is presented: a general framework for (iterative) nonlinear filtering, which uses an estimate of the spatially dependent noise variance in an image. The NOVA filter iteratively estimates the local image noise and filters the image. For the specific purpose of emphysema quantification of low-dose CT images, a dedicated, noniterative NOVA filter is constructed by using prior knowledge of the data to obtain a good estimate of the spatially dependent noise in an image. The performance of the NOVA filter is assessed by comparing characteristics of pairs of high-dose and low-dose scans. The compared characteristics are the PI scores for different thresholds and the size distributions of emphysema bullae. After filtering, the PI scores of high-dose and low-dose images agree to within 2%-3% points. The reproducibility of the high-dose bullae size distribution is also strongly improved. NOVA filtering of a CT image of typically 400 x 512 x 512 voxels takes only a couple of minutes which makes it suitable for routine use in clinical practice.     

Multiview deblurring for 3-D images from light-sheet-based fluorescence microscopy

We propose an algorithm for 3-D multiview deblurring using spatially variant point spread functions (PSFs). The algorithm is applied to multiview reconstruction of volumetric microscopy images. It includes registration and estimation of the PSFs using irregularly placed point markers (beads). We formulate multiview deblurring as an energy minimization problem subject to L1-regularization. Optimization is based on the regularized Lucy-Richardson algorithm, which we extend to deal with our more general model. The model parameters are chosen in a profound way by optimizing them on a realistic training set. We quantitatively and qualitatively compare with existing methods and show that our method provides better signal-to-noise ratio and increases the resolution of the reconstructed images.     

气动光学效应红外序列退化图像优化复原算法

从时间序列退化图像中依次连续取两帧图像来估计湍流瞬态点扩展函数,将约束优化原理应用在气动光学效应退化图像的复原过程中。针对气动光学效应湍流点扩展函数复杂多峰、随机多变等特性,在点扩展函数的估计过程中,采用保凸峰等优化策略,将点扩展函数离散值的计算转化为基于松弛迭代的最优化估计,通过极小化准则函数估计点扩展函数值,进而恢复退化图像。实验结果表明,本文方法复原效果好,速度较快。     

MR data acquisition and reconstruction using efficient sampling schemes

Fast Fourier algorithms are presented for image reconstruction from nonrectangularly sampled data. Since standard display devices require image matrices with rectangular pixels, these algorithms accept nonrectangularly sampled input and calculate output points on a rectangular array. Images are reconstructed with no loss of resolution on a 256x256 square pixel format from 224x256 hexagonally sampled raw data points with no interpolation. The images demonstrate aliasing in a hexagonal pattern around the primary image. This technique can be used to reduce scan time, data throughput, and data-storage requirements while maintaining resolution or to improve resolution while maintaining scan time.     

Bayesian pixel classification using spatially variant finitemixtures and the generalized EM algorithm

A spatially variant finite mixture model is proposed for pixel labeling and image segmentation. For the case of spatially varying mixtures of Gaussian density functions with unknown means and variances, an expectation-maximization (EM) algorithm is derived for maximum likelihood estimation of the pixel labels and the parameters of the mixture densities, An a priori density function is formulated for the spatially variant mixture weights. A generalized EM algorithm for maximum a posteriori estimation of the pixel labels based upon these prior densities is derived. This algorithm incorporates a variation of gradient projection in the maximization step and the resulting algorithm takes the form of grouped coordinate ascent. Gaussian densities have been used for simplicity, but the algorithm can easily be modified to incorporate other appropriate models for the mixture model component densities. The accuracy of the algorithm is quantitatively evaluated through Monte Carlo simulation, and its performance is qualitatively assessed via experimental images from computerized tomography (CT) and magnetic resonance imaging (MRI).     

基于各向异性规整化的总变分盲复原算法研究

针对大气湍流退化图像复原问题,提出了一种基于各向异性和非线性规整化的总变分盲复原新算法,该算法主要结合图像和湍流点扩展函数的一些性质采用基于各向异性的空间自适应规整化处理,建立了具有非线性和空间各向异性的规整化函数,使其在恢复目标图像和估计点扩展函数时能自适应地进行梯度平滑。最后,通过交替最小化方案来极小化代价函数和通过定点迭代策略将非线性方程进行线性化处理,快速地估计点扩展函数和恢复图像。在微机上对数字模拟和实际退化图像进行了一系列恢复实验,验证了算法的有效性和稳健性。     

高速运动目标的运动模糊图像复原研究

对单一图像进行运动模糊复原,存在模糊点扩散函数（PSF）难以估计以及图像反卷积的病态性问题。利用多个PSF具有联合可逆性的特点,针对运动目标观测,提出采用参数相同的多个成像设备共同对同一视场进行拍摄,来获取背景相同、曝光时间不同、目标模糊程度不同的观测图像;然后利用同一设备获取的序列图像进行目标的模糊PSF估计;并根据目标背景的运动模糊叠加特征,分别从观测图像中提取出完整的模糊目标图像;最后,对这些具有不同PSF的同一目标图像进行空间域迭代复原算式的联立求解。实验表明:该方法设计的目标获取装置对硬件条件要求较低,获取的图像更便于采用多点扩散函数联合进行图像复原,复原效果良好。     

A robust structure-adaptive hybrid vector filter for color image restoration.

A robust structure-adaptive hybrid vector filter is proposed for digital color image restoration in this paper. At each pixel location, the image vector (i.e., pixel) is first classified into several different signal activity categories by applying a modified quadtree decomposition to luminance component (image) of the input color image. A weight-adaptive vector filtering operation with an optimal window is then activated to achieve the best tradeoff between noise suppression and detail preservation. Through extensive simulation experiments conducted using a wide range of test color images, the filter has demonstrated superior performance to that of a number of well known benchmark techniques, in terms of both standard objective measurements and perceived image quality, in suppressing several distinct types of noise commonly considered in color image restoration, including Gaussian noise, impulse noise, and mixed noise.     

航天湍流退化图像的极大似然估计规整化复原算法

为了从有噪的湍流退化图像中有效地恢复出目标图像，提出了一种基于极大似然估计准则的规整化复原算法．根据图像随机场模型建立了有关多帧图像数据的对数似然函数，同时为了平滑噪声和保护图像边缘以及避免无价值的解，将一些合理的惩罚项和辅助平滑项融合到该对数似然函数中．推导出了湍流点扩展函数和目标图像的交替迭代求解公式，通过迭代方式可将点扩展函数和目标图像同时估计出来，给出了算法的并行处理方案．在微机上对强噪声条件下的湍流退化图像进行了恢复实验，实验结果表明本算法具有较强的抗噪能力和实用价值．     

Combining spatial and scale-space techniques for edge detection to provide a spatially adaptive wavelet-based noise filtering algorithm

New methods for detecting edges in an image using spatial and scale-space domains are proposed. A priori knowledge about geometrical characteristics of edges is used to assign a probability factor to the chance of any pixel being on an edge. An improved double thresholding technique is introduced for spatial domain filtering. Probabilities that pixels belong to a given edge are assigned based on pixel similarity across gradient amplitudes, gradient phases and edge connectivity. The scale-space approach uses dynamic range compression to allow wavelet correlation over a wider range of scales. A probabilistic formulation is used to combine the results obtained from filtering in each domain to provide a final edge probability image which has the advantages of both spatial and scale-space domain methods. Decomposing this edge probability image with the same wavelet as the original image permits the generation of adaptive filters that can recognize the characteristics of the edges in all wavelet detail and approximation images regardless of scale. These matched filters permit significant reduction in image noise without contributing to edge distortion. The spatially adaptive wavelet noise-filtering algorithm is qualitatively and quantitatively compared to a frequency domain and two wavelet based noise suppression algorithms using both natural and computer generated noisy images.     

双迭代等距均值滤波的医学图像恢复北大核心CSCD

医学图像中往往有很多与脉冲噪声灰度相同的像素,因此含脉冲噪声的医学图像的恢复非常困难。为了获得比现有的脉冲噪声滤波器更好的噪声抑制和纹理结构保持效果,提出了一种双迭代等距均值滤波(dual iterative equidistant mean filter,DIEMF)的医学图像恢复方法。该方法采用等距离邻域进行噪声检测和去除;噪声检测器循环地利用邻域的非最值像素与中心像素之间的平均绝对差,以及利用多数原则,将噪声像素与无噪像素区分开来;噪声去除采用自适应和双迭代的方法,以等距邻域中无噪像素和先前恢复像素的平均值作为中心噪声像素的灰度估计值,充分利用最近的先前恢复的像素。实验结果表明,该方法在噪声抑制和纹理结构保持方面优于现有的方法,特别是对于低密度噪声,它比现有的滤波器具有显著的优越性。     

Least squares approach in measurement-dependent filtering for selective medical images

An image-processing method called measurement-dependent filtering has been introduced to improve the SNR (signal-to-noise ratio) of selective images produced by various medical imaging systems. The basic algorithm involves the combination of the low-frequency information of the selective image with the high-frequency information of a nonselective image. A spatially variant control function modulates the amount of high frequency to be added at each point. A least-mean-square (LMS) control function formed from two basis images, namely the high-passed versions of the nonselective image (M(b)) and the selective image (S(b)), is introduced. The original algorithm is now viewed as a two-stage filtering method, including the low-pass filtering noise reduction and least squares filtering for the edge restoration. An appropriate linear transformation is used to convert the original basis images M(b) and S(b) into a new pair with orthogonal noise. This allows the implementation of the LMS and control function with practically obtainable a priori knowledge.     

Image restoration in computed tomography: the spatially invariant point spread function

Image restoration to deblur smoothing caused by the finite-size X-ray beam profile for a simulated computed tomography (CT) system is presented. Three simple image restoration methods are compared when the point-spread-function (PSF) is spatially invariant. In the first restoration method, an iterative least squares solution, regularized with the image norm and constrained by the boundary of the object, is obtained from the projection data. In the second method, a Wiener filter, designed using the power spectrum of CT noise, is applied to the reconstructed CT image. The third method obtains a weighted least-squares solution, by iteration, from the reconstructed CT image; the solution is regularized with the weighted image norm. Restored images were compared with the image obtained using filtered backprojection method. Differences between these images were evaluated qualitatively.     

利用拉东变换估计全景图像点扩散函数

针对全景图像点扩散函数(PSF)空间移变的特点, 提出一种利用拉东(Radon)变换估计全景图像局部区域的PSF算法。算法首先分析全景成像 原理和PSF拉东变换与图像中模糊直线响应的关系; 然后利用有效的采样方法得到孤立的采样边缘,并通过求导得到图像边缘的直线响应;最后 利用采样信息 复原出PSF并结合Lucy-Richardson(L-R)算法对图像进行复原。同时采用迭代最优 化的估计算法解决 由于采样边缘较少导致PSF估计的不准确问题。实验表明,本文算法可以有效地估 计出全景图像不同区域的PSF,有很好的工程使用价值。     

基于空间约束高斯混合模型的EPLL自然图像复原

为了提高基于块先验的自然图像复原效果,有效去除图像中的噪声和模糊,提出了一种基于空间约束高斯混合模型的块似然对数期望(Expected Patch Log Likelihood, EPLL)复原框架。基于图像块的空间分布信息,将图像块的空间约束高斯混合统计特性作为先验,在图像块复原的基础上实现整幅图像的全局优化复原。对比相关的图像复原方法,提出的方法去噪和去模糊效果更好,并且保图像细节。利用客观性能指标对复原结果进行评价。实验结果表明,提出的方法有效易行,而且复原图像表现出良好的可视效果。     

Spatially adaptive wavelet-based multiscale image restoration

In this paper, we present a new spatially adaptive approach to the restoration of noisy blurred images, which is particularly effective at producing sharp deconvolution while suppressing the noise in the flat regions of an image. This is accomplished through a multiscale Kalman smoothing filter applied to a prefiltered observed image in the discrete, separable, 2-D wavelet domain. The prefiltering step involves constrained least-squares filtering based on optimal choices for the regularization parameter. This leads to a reduction in the support of the required state vectors of the multiscale restoration filter in the wavelet domain and improvement in the computational efficiency of the multiscale filter. The proposed method has the benefit that the majority of the regularization, or noise suppression, of the restoration is accomplished by the efficient multiscale filtering of wavelet detail coefficients ordered on quadtrees. Not only does this lead to potential parallel implementation schemes, but it permits adaptivity to the local edge information in the image. In particular, this method changes filter parameters depending on scale, local signal-to-noise ratio (SNR), and orientation. Because the wavelet detail coefficients are a manifestation of the multiscale edge information in an image, this algorithm may be viewed as an "edge-adaptive" multiscale restoration approach.     

一种新的像素级多聚焦图像融合算法

该文在小波变换的基础上提出了一种将一维自组织特征映射(SOFM)网络和进化策略相结合的多聚焦图像融合算法。该方法对不同聚焦点的图像进行冗余小波分解,再分别将其各方向、各尺度的高频信息进行叠加,并在高频信息叠加层上提取反映图像清晰度差异的归一化特征图,依据此特征图,使用SOFM网络对原始图像像素进行分类,并利用进化策略对各类像素求出最优的融合系数。实验结果表明该算法比拉普拉斯变换法和小波变换法具有更好的融合效果。