改进的固定点图像复原算法（英文）

研究了周期边界条件下,Tikhonov正则化的固定点算法,提出了变化正则化参数的方法。首先对正则化参数取较大值,抑制复原图像中的噪声,通过得出的收敛结果来修正初始梯度;然后对正则化参数取较小值,以增强复原图像中的细节。实验结果表明,与当前求解L1范数正则化函数和全变分正则化函数的流行算法比较,本文算法对于运动模糊与高斯模糊图像的复原效果更佳。     

基于加权块稀疏联合非凸低秩约束的高光谱图像去条带方法

针对高光谱图像(hyperspectral images,HSI)去条带易引起影像结构细节丢失问题,提出一种基于加权块稀疏(weighted block sparsity,WBS)正则化联合最小最大非凸惩罚(minimax concave penalty,MCP)约束的HSI去条带方法.本算法采用加权?2,1范数和MC...     

A V-curve criterion for the parameter optimization of the Tikhonov regularization inversion algorithm for particle sizing

The regularization parameter plays an important role in applying the Tikhonov regularization method to recover the particle size distribution from dynamic light scattering experiments. The so-called V-curve, which is a plot of the product of the residual norm and the norm of the recovered distribution versus all valid regularization parameters, can be used to estimate the result of inversion. Numerical simulation demonstrated that the resultant V-curve can be applied to optimize the regularization parameter. The regularization parameter is optimized corresponding to the minimum value of the V-curve. Simulation and experimental results show that stable distributions can be retrieved using the Tikhonov regularization with optimum parameter for unimodal particle size distributions.     

基于 L-曲线参数优化的均匀声场重建算法

为了得到最小二乘法声场重建问题的稳定解,通常需要引入Tikhonov正则化方法。然而正则化程度取决于正则化参数的选择。针对这一问题,提出了一种基于L-曲线法参数选择的均匀声场重建算法。该算法根据重建误差与扬声器功率计算得到L-曲线,该曲线上曲率最大的点所对应的参数值作为Tikhonov正则化参数的选值。确定正则化参数后可进一步得到扬声器权系数以及重建均匀声场。针对不同正则化参数取值方法,对控制区域进行均匀声场重建以及重建性能仿真。仿真结果及实验表明,L-曲线法实现了重建误差与扬声器驱动信号功率之间的平衡。     

Hopfield neural network-based image restoration with adaptive mixed-norm regularization

To overcome the shortcomings of traditional image restoration model and total variation image restoration model, we propose a novel Hopfield neural network-based image restoration algorithm with adaptive mixed-norm regularization. The new error function of image restoration combines the L2-norm and L1- norm regularization types. A method of calculating the adaptive scale control parameter is introduced. Experimental results demonstrate that the proposed algorithm is better than other algorithms with single norm regularization in the improvement of signal-to-noise ratio （ISNR） and vision effect.     

Structural source identification using a generalized Tikhonov regularization

This paper addresses the problem of identifying mechanical exciting forces from vibration measurements. The proposed approach is based on a generalized Tikhonov regularization that allows taking into account prior information on the measurement noise as well as on the main characteristics of sources to identify like its sparsity or regularity. To solve such a regularization problem efficiently, a Generalized Iteratively Reweighted Least-Squares (GIRLS) algorithm is introduced. Proposed numerical and experimental validations reveal the crucial role of prior information in the quality of the source identification and the performance of the GIRLS algorithm.     

Application of perceptual difference model on regularization techniques of parallel MR imaging

Parallel magnetic resonance imaging through sensitivity encoding using multiple receiver coils has emerged as an effective tool to reduce imaging time or to improve image SNR. The quality of reconstructed images is limited by the inaccurate estimation of the sensitivity map, noise in the acquired k-space data and the ill-conditioned nature of the coefficient matrix. Tikhonov regularization is a popular method to reduce or eliminate the ill-conditioned nature of the problem. In this approach, selection of the regularization map and the regularization parameter is very important. Perceptual difference model (PDM) is a quantitative image quality evaluation tool that has been successfully applied to varieties of MR applications. High correlation between the human rating and PDM score shows that PDM should be suitable to evaluate image quality in parallel MR imaging. By applying PDM, we compared four methods of selecting the regularization map and four methods of selecting the regularization parameter. We found that a regularization map obtained using generalized series (GS) together with a spatially adaptive regularization parameter gave the best reconstructions. PDM was also used as an objective function for optimizing two important parameters in the spatially adaptive method. We conclude that PDM enables one to do comprehensive experiments and that it is an effective tool for designing and optimizing reconstruction methods in parallel MR imaging.     

Nonlocal regularization based on DT-CWT for WMSN video image iterative reconstruction

The prior knowledge of signal is the previous condition of image compressed sensing reconstruction. In order to improve the quality of the priors except for image sparsity, this paper proposes a new model of video image reconstruction. The texture is the important visual feature of video image as a result of its repeat, leading to image global geometrical structures. The nonlocal idea comes from image self-familiar and can represent image detail features from the geometrical point of view. Therefore, the texture geometrical feature of video image is researched, and we take advantage of dual-tree complex wavelet transform to portray the sparsity representation regularization of the texture. What is more, global constrained regularization is constructed with the help of the nonlocal idea. On the basis of the two regularizations above, a new reconstruction model of video image compressed sensing is proposed, which not only preserves the sparsity prior knowledge of image but also improves the quality of prior knowledge of image by promoting geometrical structure. Iterative shrinkage thresholding algorithm is adopted to solve the model leading to a both simple and quick iterative algorithm. Numerical experiments show that our method is efficient for video image recovery, especially preserving the global details of the original video image.     

基于迭代Tikhonov正规化的三刺激值重建光谱方法研究

光谱图像中的反射率光谱数据维数高,且与光源、设备均无关,能够比较全面、真实、客观地描述图像中物体的颜色信息。针对三色相机的光谱图像获取系统中三维色度数据重建多维光谱数据产生的光谱信息丢失、以及伴随而生的颜色信息丢失问题,提出了迭代Tikhonov正规化的光谱重建方法。首先依据色度学理论中色度值与反射率光谱之间的关系,构建反射率光谱重建方程建立起相机所获三维色度数据与高维反射率光谱数据的映射关系;然后,通过反射率光谱重建方程的病态分析,在Moore-Penrose伪逆矩阵求解思想的基础上构建迭代Tikhonov正规化方法求解反射率光谱,并利用训练样本数据通过L-曲线方法训练获取迭代Tikhonov正规化的最优正规化参数,以有效控制并改善反射率光谱重建方程求解的病态、减少重建光谱的光谱信息丢失。实验通过选取样本数据对光谱重建方法进行验证。验证实验的结果表明所提出的光谱重建方法改善了三色相机的光谱图像获取系统中重建光谱的光谱信息丢失程度,使得重建光谱的光谱误差和色度误差较其他光谱重建方法均有明显降低。     

Adaptive fixed-point iterative shrinkage/thresholding algorithm for MR imaging reconstruction using compressed sensing

Recently compressed sensing (CS) has been applied to under-sampling MR image reconstruction for significantly reducing signal acquisition time. To guarantee the accuracy and efficiency of the CS-based MR image reconstruction, it necessitates determining several regularization and algorithm-introduced parameters properly in practical implementations. The regularization parameter is used to control the trade-off between the sparsity of MR image and the fidelity measures of k-space data, and thus has an important effect on the reconstructed image quality. The algorithm-introduced parameters determine the global convergence rate of the algorithm itself. These parameters make CS-based MR image reconstruction a more difficult scheme than traditional Fourier-based method while implemented on a clinical MR scanner. In this paper, we propose a new approach that reveals that the regularization parameter can be taken as a threshold in a fixed-point iterative shrinkage/thresholding algorithm (FPIST) and chosen by employing minimax threshold selection method. No extra parameter is introduced by FPIST. The simulation results on synthetic and real complex-valued MRI data show that the proposed method can adaptively choose the regularization parameter and effectively achieve high reconstruction quality. The proposed method should prove very useful for practical CS-based MRI applications.     

The application of regularization technique based on partial optimization in the nearfield acoustic holography

The regularization technique for stabilizing the reconstruction based on the nearfield acoustic holography(NAH) was investigated on the basis of the equivalent source method.In order to obtain higher regularization effect,a regularization method based on the idea of partial optimization was proposed,which inherits the advantages of the Tikhonov and another regularization method—truncated singular value decomposition(TSVD).Through the numerical simulation,it is proved that the proposed method is stabler than the Tikhonov,and more precise than the TSVD.Finally the validity and the feasibility of the proposed method are demonstrated by an experiment carried out in a semi-anechoic room with two speakers.     

Smoothly Clipped Absolute Deviation (SCAD) regularization for compressed sensing MRI Using an augmented Lagrangian scheme

PurposeCompressed sensing (CS) provides a promising framework for MR image reconstruction from highly undersampled data, thus reducing data acquisition time. In this context, sparsity-promoting regularization techniques exploit the prior knowledge that MR images are sparse or compressible in a given transform domain. In this work, a new regularization technique was introduced by iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm with the aim of reducing the sampling rate even lower than it is required by the conventional l₁ norm while approaching an l₀ norm.Materials and MethodsThe CS-MR image reconstruction was formulated as an equality-constrained optimization problem using a variable splitting technique and solved using an augmented Lagrangian (AL) method developed to accelerate the optimization of constrained problems. The performance of the resulting SCAD-based algorithm was evaluated for discrete gradients and wavelet sparsifying transforms and compared with its l₁-based counterpart using phantom and clinical studies. The k-spaces of the datasets were retrospectively undersampled using different sampling trajectories. In the AL framework, the CS-MRI problem was decomposed into two simpler sub-problems, wherein the linearization of the SCAD norm resulted in an adaptively weighted soft thresholding rule with a sparsity enhancing effect.ResultsIt was demonstrated that the proposed regularization technique adaptively assigns lower weights on the thresholding of gradient fields and wavelet coefficients, and as such, is more efficient in reducing aliasing artifacts arising from k-space undersampling, when compared to its l₁-based counterpart.ConclusionThe SCAD regularization improves the performance of l₁-based regularization technique, especially at reduced sampling rates, and thus might be a good candidate for some applications in CS-MRI.     

The reconstruction of particle size distributions from dynamic light scattering data using particle swarm optimization techniques with different objective functions

In this paper, the reconstruction of particle size distributions (PSDs) using particle swarm optimization (PSO) techniques from dynamic light scattering (DLS) data was established. Three different objective functions containing non-smooth constrained objective function, smooth functional objective function of Tikhonov regularization and L objective function, were employed. Simulated results of unimodal, bimodal and bi-dispersed particles show that the PSO technique with non-smooth constrained objective function produces narrower PSDs focusing on peak position in the presence of random noise, the PSO technique with smooth functional of Tikhonov regularization creates relative smooth PSDs, which could be successfully applied to the broad particles inversion, and the PSO technique with L objective function yields smooth PSDs, which saves calculation amount. Experimental results as well as comparisons with CONTIN algorithm and Cumulants method demonstrate the performance of our algorithms. Therefore, the PSO techniques employing the three different objective functions, which only require objective function and need a few initial guesses, may be applied to the reconstruction of PSDs from DLS data.     

基于L1范数和正交梯度算子的超分辨率重建

针对超分辨率图像重建的病态问题,设计了一种新的自适应超分辨率图像序列重建算法。该算法在L1范数重建框架下,利用金字塔算法与Lucas-Kanade算法相结合的方法实现图像配准,获得亚像素的运动估计;通过引入移位算子给出了基于正交梯度算子的正则项的实现方法,并从自适应的角度选择正则化参数,最后通过最速下降法求解模型的目标泛函最小值。结果表明:对于模拟实验和真实序列实验,该方法相比于样条插值算法、Tikhonov正则化算法、双边全变差重建算法都有一定的优势,能够取得更好的复原效果,并且由于正则项较为简单,重建所需时间相对减少。     

Acoustical inverse problems regularization: Direct definition of filter factors using Signal-to-Noise Ratio

Acoustic imaging aims at localization and characterization of sound sources using microphone arrays. In this paper a new regularization method for acoustic imaging by inverse approach is proposed. The method first relies on the singular value decomposition of the plant matrix and on the projection of the measured data on the corresponding singular vectors. In place of regularization using classical methods such as truncated singular value decomposition and Tikhonov regularization, the proposed method involves the direct definition of the filter factors on the basis of a thresholding operation, defined from the estimated measurement noise. The thresholding operation is achieved using modified filter functions. The originality of the approach is to propose the definition of a filter factor which provides more damping to the singular components dominated by noise than that given by the Tikhonov filter. This has the advantage of potentially simplifying the selection of the best regularization amount in inverse problems. Theoretical results show that this method is comparatively more accurate than Tikhonov regularization and truncated singular value decomposition.     

基于弹性变分模态分解的癫痫脑电信号分类方法

癫痫脑电信号分类对于癫痫诊治具有重要意义.为了实现病灶性与非病灶性癫痫脑电信号的分类,本文利用弹性网回归重构变分模态分解算法,提出弹性变分模态分解算法并将其应用到所提癫痫脑电信号分类方法中.该方法先将原信号分割成多个子信号,并对各子信号进行弹性变分模态分解,然后从分解后的不同变分模态函数中提取精细复合多尺度散布熵作为特征,最后利用支持向量机进行分类.针对癫痫脑电的公共数据集,最终的实验结果表明,准确率、灵敏度和特异度三个性能指标分别达到92.54%,93.22%和91.86%.     

Method of fundamental solutions with optimal regularization techniques for the Cauchy problem of the Laplace equation with singular points

The purpose of this study is to propose a high-accuracy and fast numerical method for the Cauchy problem of the Laplace equation. Our problem is directly discretized by the method of fundamental solutions (MFS). The Tikhonov regularization method stabilizes a numerical solution of the problem for given Cauchy data with high noises. The accuracy of the numerical solution depends on a regularization parameter of the Tikhonov regularization technique and some parameters of the MFS. The L-curve determines a suitable regularization parameter for obtaining an accurate solution. Numerical experiments show that such a suitable regularization parameter coincides with the optimal one. Moreover, a better choice of the parameters of the MFS is numerically observed. It is noteworthy that a problem whose solution has singular points can successfully be solved. It is concluded that the numerical method proposed in this paper is effective for a problem with an irregular domain, singular points, and the Cauchy data with high noises.     

Spectral semi-blind deconvolution with hybrid regularization

A spectral semi-blind deconvolution with hybrid regularization (SBD-HR) is proposed to recover the spectrum and to estimate the parameter of the point spread function (PSF) adaptively. Firstly, a weighted Tikhonov regularization term about the spectrum is presented to preserve the details of spectrum. Then the regularization term about the PSF is modeled as L1-norm instead of L2-norm to enhance the stability of kernel estimation. The numerical solution processes for recovering the spectrum and for estimating the parameter of the PSF are deduced. Simulation results of infrared spectrum deconvolution demonstrate that the proposed method can recover the spectrum better from the degraded spectrum and estimate the parameter of the PSF accurately.     

Linear Tikhonov regularization against an edge field: an improved reconstruction algorithm in photothermal depth profilometry

This work introduces the concept of edge-field regularization into photothermal inverse depth profilometry problems. An edge field allows prior information concerning the depth location of material interfaces in a sample to be introduced into a Tikhonov regularization problem by a simple binary encoding. The edge-field regularization allows Nth-order Tikhonov stabilization constraints to be applied independently to multiple zones or segments of a depth profile between defined interface positions. This allows the reconstruction of continuous depth-profile information within known layers, without the globally imposed smoothing and edge oscillations of the classical regularization methods. This method successfully reconstructs both the amplitude of the interface discontinuities and the photothermal depth-contrast variations within the bounding edges, to a resolution limited by the resolving kernel for the underlying Nth-order Tikhonov constraint. The edge-field regularization dramatically reduces the errors associated with profiling photothermal contrast in bounded zones that are depth-displaced in the sample. Received: 19 September 2002 / Published online: 5 May 2003 RID="*" ID="*"Corresponding author. Fax: +1-514/398-3797, E-mail: joan.power@mcgill.ca