An algorithm for sparse MRI reconstruction by Schatten p-norm minimization

In recent years, there has been a concerted effort to reduce the MR scan time. Signal processing research aims at reducing the scan time by acquiring less K-space data. The image is reconstructed from the subsampled K-space data by employing compressed sensing (CS)-based reconstruction techniques. In this article, we propose an alternative approach to CS-based reconstruction. The proposed approach exploits the rank deficiency of the MR images to reconstruct the image. This requires minimizing the rank of the image matrix subject to data constraints, which is unfortunately a nondeterministic polynomial time (NP) hard problem. Therefore we propose to replace the NP hard rank minimization problem by its nonconvex surrogate — Schatten p-norm minimization. The same approach can be used for denoising MR images as well.Since there is no algorithm to solve the Schatten p-norm minimization problem, we derive an efficient first-order algorithm. Experiments on MR brain scans show that the reconstruction and denoising accuracy from our method is at par with that of CS-based methods. Our proposed method is considerably faster than CS-based methods.     

Dynamic MRI reconstruction from highly undersampled (k,t)-space data using weighted Schatten p-norm regularizer of tensor

Combination of the low-rankness and sparsity has been successfully used to reconstruct desired dynamic magnetic resonance image (MRI) from highly-undersampled (k, t)-space data. However, nuclear norm, as a convex relaxation of the rank function, can cause the solution deviating from the original solution of low-rank problem. Moreover, equally treating different rank component is not flexible to deal with real applications. In this paper, an efficient reconstruction model is proposed to efficiently reconstruct dynamic MRI. First, we treat dynamic MRI as a 3rd-order tensor, and formulate the low-rankness via non-convex Schatten p-norm of matrices unfolded from the tensor. Secondly, we assign different weight for each rank component in Schatten p-norm. Furthermore, we combine the proposed weighted Schatten p-norm of a tensor as low-rank regularizer, and spatiotemporal total variation as sparse regularizer to formulate the reconstruction model for dynamic MRI. Thirdly, to efficiently solve the formulated reconstruction model, we derive an algorithm based on Bregman iterations with alternating direction multiplier. Over two public data sets of dynamic MRI, experiments demonstrate that the proposed method achieves much better quality.     

Motion deblurring using edge map with blurred/noisy image pairs

Motion deblurring methods using blurred/noisy image pairs usually include denoising process of the noisy image. Because both remaining noise and distorted fine details in the denoised image cause an error on deblurring, we propose an algorithm using an edge map of the noisy image to retain sharp edge information while neglecting noise in any smooth region that does not contain information about the motion that occurred during the exposure. In addition, the blur kernel is efficiently estimated by employing the fast total variation regularization method for the gradients of blurred and noisy images only on edge regions. For latent image restoration, another fidelity term is added, which compares the gradients of the noisy and estimated latent images on edge regions to preserve the fine details of the noisy image. To model a sparse distribution of real-world image gradients, a deconvolution method imposing hyper-Laplacian priors based on an alternating minimization scheme is also derived to restore a latent image efficiently. Experimental results show that the peak signal-to-noise ratios of the restored images against the original latent images have been increased by 11.1% on average, when compared to the existing algorithms using an image pair.     

Non-local means algorithm with adaptive patch size and bandwidth

Non-local means algorithm is an effective denoising method that consists in some kind of averaging process carried on similar patches in a noisy image. Some internal parameters, such as patch size and bandwidth, strongly influence the performance of non-local means, but with the difficulty of tuning. Many solutions for choosing these two parameters, like cross-validation and Steins unbiased risk estimate criterion, are successful but computationally heavy. In this paper, we introduce a new feature metric that is capable of providing a quantitative measure of geometric structures of image in the presence of noise. The proposed region-based non-local means method first classifies a noisy image into several regions. Then, a local window and a local bandwidth value are selected pixel-wisely according to the property of each region and the local value of the new feature metric. Experiments on standard test images show that the proposed method outperforms the original non-local means version by around 1.34 dB and is comparable to or better than the performance of the current state-of-the-art non-local means based denoising algorithms, both visually and quantitatively.     

Exploiting rank deficiency and transform domain sparsity for MR image reconstruction

The reconstruction of magnetic resonance (MR) images from the partial samples of their k-space data using compressed sensing (CS)-based methods has generated a lot of interest in recent years. To reconstruct the MR images, these techniques exploit the sparsity of the image in a transform domain (wavelets, total variation, etc.). In a recent work, it has been shown that it is also possible to reconstruct MR images by exploiting their rank deficiency. In this work, it will be shown that, instead of exploiting the sparsity of the image or rank deficiency alone, better reconstruction results can be achieved by combining transform domain sparsity with rank deficiency.To reconstruct an MR image using its transform domain sparsity and its rank deficiency, this work proposes a combined l₁-norm (of the transform coefficients) and nuclear norm (of the MR image matrix) minimization problem. Since such an optimization problem has not been encountered before, this work proposes and derives a first-order algorithm to solve it.The reconstruction results show that the proposed approach yields significant improvements, in terms of both visual quality as well as the signal to noise ratio, over previous works that reconstruct MR images either by exploiting rank deficiency or by the standard CS-based technique popularly known as the ‘Sparse MRI.’     

旋转不变的非局域均值算法在磁共振图像去噪中的应用

磁共振成像（MRI）实验时常采用多次扫描累加平均提高图像信噪比（SNR）,但当扫描过程中运动引起图像变形时,简单地累加平均就无法奏效.为此,本研究组曾提出一种匹配加权平均方法（MWA）提高图像的信噪比.在此基础上,该文提出一种旋转不变的非局域均值算法（RINLM）,即选取圆形邻域区域并将其划分为一系列以中心像素为圆心的等面积圆环,再计算模式的相似性.RINLM算法可以更好地利用图像中旋转的冗余信息、找到更多的相似结构,提高算法的去噪性能.我们把该方法应用于低信噪比图像序列的平均和去噪中,可以更好地处理旋转的局部运动.与非局域均值算法（NLM）相比,RINLM算法可以进一步提高图像的信噪比;与MWA方法相比,其与RINLM算法的结合可以进一步提高磁共振图像序列信噪比,更好的保持图像边缘信息.     

Intensity image denoising for laser active imaging system using nonsubsampled contourlet transform and SURE approach

This paper presents an algorithm based on nonsubsampled contourlet transform (NSCT) and Stein's unbiased risk estimate with a linear expansion of thresholds (SURE-LET) approach for intensity image denoising. First, we analyzed the multiplicative noise model of intensity image and make the non-logarithmic transform on the noisy signal. Then, as a multiscale geometric representation tool with multi-directivity and shift-invariance, NSCT was performed to capture the geometric information of images. Finally, SURE-LET strategy was modified to minimize the estimation of the mean square error between the clean image and the denoised one in the NSCT domain. Experiments on real intensity images show that the algorithm has excellent denoising performance in terms of the peak signal-to-noise ratio (PSNR), the computation time and the visual quality.     

基于小波包分析二次阈值去噪图像复原方法

提出了基于小波包分析的二次去噪复原的图像复原新方法。利用小波包分析在信号去噪中对图像信号高频部分更加灵活、更加精确的局部分析能力,针对低信噪比模糊图像,通过选取较小的阈值,交替地进行了两次预去噪处理和复原。采用PML算法,实验比较了小波包阈值一次去噪法和二次去噪法。实验表明,二次去噪法由于阈值取值较小,对退化图像信息的能量分布改变较小,可以获得比一次去噪法更加良好的复原效果。     

Image denoising using trivariate prior model in nonsubsampled dual-tree complex contourlet transform domain and non-local means filter in spatial domain

Image denoising is always the basic problem of image processing, and the main challenge is how to effectively remove the noise and preserve the detailed information. This paper presents a new image denoising algorithm based on the combination of trivariate prior model in nonsubsampled dual-tree complex contourlet transformlet transform (NSDTCT) domain and non-local means filter (NLMF) in spatial domain. Firstly, NSDTCT is constructed by combining the dual-tree complex wavelet transform (DTCWT) and nonsubsampled directional filter banks (NSDFB). The noisy image is decomposed by using NSDTCT. Secondly, based on the correlation between the interscale and intrascale dependencies of NSDTCT coefficients, the distribution of the high frequency coefficients is modeled with the trivariate non-Gaussian distribution model. A nonlinear trivariate shrinkage function is derived in the framework of Bayesian theory, and then the denoised coefficients are obtained and inverse NSDTCT is performed to get the initial denoised image. Finally, NLMF is used to smooth the initial denoised image. Simulation experiment shows that our algorithm can obtain better performances than those outstanding denoising algorithms in terms of peak signal-to-noise ratio (PSNR), mean structural similarity (MSSIM) as well as visual quality.     

Improved dynamic MRI reconstruction by exploiting sparsity and rank-deficiency

In this paper we address the problem of dynamic MRI reconstruction from partially sampled K-space data. Our work is motivated by previous studies in this area that proposed exploiting the spatiotemporal correlation of the dynamic MRI sequence by posing the reconstruction problem as a least squares minimization regularized by sparsity and low-rank penalties. Ideally the sparsity and low-rank penalties should be represented by the l₀-norm and the rank of a matrix; however both are NP hard penalties. The previous studies used the convex l₁-norm as a surrogate for the l₀-norm and the non-convex Schatten-q norm (0 < q ≤ 1) as a surrogate for the rank of matrix. Following past research in sparse recovery, we know that non-convex l_p-norm (0 < p ≤ 1) is a better substitute for the NP hard l₀-norm than the convex l₁-norm. Motivated by these studies, we propose improvements over the previous studies by replacing the l₁-norm sparsity penalty by the l_p-norm. Thus, we reconstruct the dynamic MRI sequence by solving a least squares minimization problem regularized by l_p-norm as the sparsity penalty and Schatten-q norm as the low-rank penalty. There are no efficient algorithms to solve the said problems. In this paper, we derive efficient algorithms to solve them. The experiments have been carried out on Dynamic Contrast Enhanced (DCE) MRI datasets. Both quantitative and qualitative analysis indicates the superiority of our proposed improvement over the existing methods.     

基于梯度和小波变换的水下距离选通图像去噪

水体的散射效应、激光光斑、成像器件的非理想化等因素使得图像出现大量无规律粒状噪声,它们增加了水下距离选通图像的背景噪声,模糊了目标轮廓,掩盖了目标细节,降低了图像的信噪比。针对上述问题本文提出了一种基于梯度和小波变换的去噪方法。首先对图像进行余弦小波变换,得到不同频率空间的图像集。低频空间引入新的图像梯度强化方法以提高图像的纹理信息量;对应非均匀性条带的LH或HL空间做曲面拟合处理以消除非均匀性条带的影响;在HH空间去噪过程中,低层空间做非局部均值处理以保留图像相似信息,高层空间做分数阶积分处理以保留图像细节信息。最后小波逆变换得到结果图像。从实验水槽中采集水下图像进行算法验证,将改进方法与已有算法比对分析。实验表明,本文所研究的水下去噪算法,能够平滑噪声且更大限度地保留图像细节纹理,在客观评价指标上提升了6%。     

Denoising 3D MR images by the enhanced non-local means filter for Rician noise

The non-local means (NLM) filter removes noise by calculating the weighted average of the pixels in the global area and shows superiority over existing local filter methods that only consider local neighbor pixels. This filter has been successfully extended from 2D images to 3D images and has been applied to denoising 3D magnetic resonance (MR) images. In this article, a novel filter based on the NLM filter is proposed to improve the denoising effect. Considering the characteristics of Rician noise in the MR images, denoising by the NLM filter is first performed on the squared magnitude images. Then, unbiased correcting is carried out to eliminate the biased deviation. When performing the NLM filter, the weight is calculated based on the Gaussian-filtered image to reduce the disturbance of the noise. The performance of this filter is evaluated by carrying out a qualitative and quantitative comparison of this method with three other filters, namely, the original NLM filter, the unbiased NLM (UNLM) filter and the Rician NLM (RNLM) filter. Experimental results demonstrate that the proposed filter achieves better denoising performance over the other filters being compared.     

基于K-SVD和残差比的低信噪比图像稀疏表示去噪算法

针对低信噪比图像去噪问题,提出了一种基于K-SVD(Singular Value Decomposition)和残差比(Residual Ratio Iteration Termination)的正交匹配追踪(Orthogonal Matching Pursuit,OMP)图像稀疏分解去噪算法。该算法利用K-SVD算法将离散余弦变换(Discrete cosine transform,DCT)框架产生的冗余字典训练成能够有效反映图像结构特征的超完备字典,以实现图像的有效表示。然后以残差比作为OMP算法迭代的终止条件来实现图像的去噪。实验表明,该算法相对于传统基于Symlets小波图像去噪、基于Contourlet变换的图像去噪,以及基于DCT冗余字典的稀疏表示图像去噪,能够更加有效地滤除低信噪比图像中的高斯白噪声,保留原图像的有用信息。     

Content-based adaptive image denoising using spatial information

The maximum a posteriori (MAP) model is widely used in image processing fields, such as denoising, deblurring, segmentation, reconstruction, and others. However, the existing methods usually employ a fixed prior item and regularization parameter for the whole image and ignore the local spatial adaptive properties. Though the non-local total variation model has shown great promise because of exploiting the correlation in the image, the computation cost and memory load are the issues. In this paper, a content-based local spatial adaptive denoising algorithm is proposed. To realize the local spatial adaptive process of the prior model and regularization parameter, first the degraded image is divided into several same-sized blocks and the Tchebichef moment is used to analyze the local spatial properties of each block. Different property prior items and regularization parameters are then applied adaptively to different properties’ blocks. To reduce the computational load in denoising process, the split Bregman iteration algorithm is employed to optimize the non-local total variation model and accelerate the speed of the image denoising. Finally, a set of experiments and performance evaluation using recent image quality assessment index are provided to assess the effectiveness of the proposed method.     

Non-local and nonlinear background suppression method controlled by multi-scale clutter metric

To improve the detection performance for non-morphological multi-scale target in IR image containing complex cloud clutter, on basis of cloud scenario self-similarity feature, a non-local and nonlinear background suppression algorithm controlled by multi-scale clutter metric is presented. According to the classical achievements on cloud structure, self-similarity and relativity of cloud clutter on image for target detection is deeply analyzed by classical indicators firstly. Then we establish multi-scale clutter metric method based on LoG operator to describe scenes feature for controlled suppression method. After that, non-local means based on optimal strength similarity metric as non-local processing, and multi-scale median filter and on minimum gradient direction as local processing are set up. Finally linear fusing principle adopting clutter metric for local and non-local processing is put forward. Experimental results by two kinds of infrared imageries show that compared with classical and similar methods, the proposed method solves the existing problems of targets energy attenuation and suppression degradation in strongly evolving regions in previous methods. By evaluating indicators, the proposed method has a superior background suppression performance by increasing the BSF and ISCR 2 times at least.     

基于3D卷积自编解码器和低秩表示的高光谱异常检测

针对高光谱影像数据维度高、空间和光谱信息利用不足以及局部结构特征表达有限等问题,提出了一种基于3D卷积自编解码器和低秩表示的高光谱异常检测算法。首先,通过3D卷积自编解码器提取高光谱影像的空谱特征,并针对高光谱图像的局部区域强相关性,设计了一种新的损失函数来约束中心像素和周围像素,以提取判别性较强的特征图;然后,针对所提取的特征图,通过基于密度的空间聚类算法构建背景字典,并利用低秩表示分离出异常区域;最后,融合由3D卷积自编解码器得到的重构误差和异常区域检测结果,得到最终检测图并为异常目标关键信息的挖掘提供依据。为了验证所提算法的有效性,在两个真实的机场高光谱数据集上进行飞机等目标检测实验,ROC、AUC量化指标和主观分析等实验结果表明,与其它6种异常检测算法相比,本文算法具有更高的异常目标检测精度。     

运动与离焦模糊图像的复原

在运动和离焦所引起的图像模糊的情况中,本文提出了一种新的基于霍夫变换区分离焦模糊和运动模糊两类模糊的方法.该方法通过比较霍夫变换矩阵中的亮点数来区分两类模糊,不仅正确率达到100%,而且抗干扰性能好;其次通过对运动模糊图像做两次方向微分,估计其模糊方向,提高了模糊方向的估计准确度;最后利用改进的Prewiit算子和费米函数计算模糊图像的刃边函数,进而得到图像的调制传递函数,再利用维纳滤波复原图像.实验结果表明:本文算法不仅具有有效性和强抗噪音能力,而且对图像的信噪比要求可以低到20 dB;与传统算法相比,提高了图像的复原质量.     

基于噪声特性的大气湍流退化图像多帧盲反卷积复原

由于大气湍流和噪声的影响,造成观测目标图像的退化.为了目标的精确观测,根据噪声特性,结合符合物理意义的约束条件,提出了新的大气湍流图像盲反卷积复原最小化模型,并以共轭梯度数值优化方法交替迭代求解,复原观测目标图像.为验证提出的算法的有效性,在计算机上模拟参数为望远镜口径为2.0 m,大气相干长度为0.1 m,图像信噪比为10 dB的大气湍流退化和噪声污染的图像,以提出的盲反卷积复原方法复原,实验结果表明,提出的盲反卷积复原算法避免了传统的盲反卷积复原算法的缺陷,有效地克服大气湍流和噪声的影响,复原出了清晰的观测目标图像.该图像盲反卷积复原方法的研究,对地基望远镜的观测有重要的基础性作用.     

Fusion method of infrared and visible images based on neighborhood characteristic and regionalization in NSCT domain

On fusing infrared and visible image, the traditional fusion method cannot get the better image quality. Based on neighborhood characteristic and regionalization in NSCT (Nonsubsampled Contourlet Transform) domain, the fusion algorithm was proposed. Firstly, NSCT was adopted to decompose infrared and visible images at different scales and directions for the low and high frequency coefficients, the low frequency coefficients which were fused with improving regional weighted fusion method based on neighborhood energy, and the high-frequency coefficients were fused with multi-judgment rule based on neighborhood characteristic regional process. Finally, the coefficients were reconstructed to obtain the fused image. The experimental results show that, compared with the other three related methods, the proposed method can get the biggest value of IE (information entropy), MI(VI,F) (mutual information from visible image), MI(VI,F) (mutual information from infrared image), MI (sum of mutual information), and Q^AB/F (edge retention). The proposed method can leave enough information in the original images and its details, and the fused images have better visual effects.     

A face recognition algorithm based on collaborative representation

In this paper, we propose a face recognition algorithm by incorporating a neighbor matrix into the objective function of sparse coding. We first calculate the neighbor matrix between the test sample and each training sample by using the revised reconstruction error of each class. Specifically, the revised reconstruction error (RRE) of each class is the division of the l₂-norm of reconstruction error to the l₂-norm of reconstruction coefficients, which can be used to increase the discrimination information for classification. Then we use the neighbor matrix and all the training samples to linearly represent the test sample. Thus, our algorithm can preserve locality and similarity information of sparse coding. The experimental results show that our algorithm achieves better performance than four previous algorithms on three face databases.