基于小波变换和非负支撑域递归逆滤波算法的盲目图像复原

提出了一种将自适应正则化方法与非负支撑域递归逆滤波(NAS-RIF)算法相结合用于小波域的盲图像复原算法.该算法先对降质图像进行小波分解,得到了图像在不同子频段的信息.在各个子频段采用NAS-RIF算法进行复原.针对各个子频段内图像的频率和方向特性,分别引入了不同的正则化约束项.在各个子频段估计出噪声方差,提出了根据噪声方差和图像局部方差来选取正则化参数.分别对两幅模糊图像进行了仿真实验,复原结果取得的信噪比分别为19.66 dB和23.86 dB.实验结果表明,复原效果相对于空间自适应正则化方法有一定的提高.     

Improving the resolution of functional brain imaging: analyzing functional data in anatomical space

The accurate mapping of functional magnetic resonance imaging (fMRI) activations to anatomical structures is critical for fMRI studies of brain organization. In the commonly used functional space analysis method, functional images are realigned to a functional reference image and processed in low-resolution functional space. The average functional activations are then projected into high-resolution anatomical space for visualization. Here, we describe a new technique, anatomical space analysis (ASA), whereby low-resolution functional images are first coregistered and resampled directly into high-resolution anatomical space with all subsequent data processing performed in high-resolution space. A major advantage of ASA is that minor scanner sampling instabilities and small head movements can increase spatial resolution by providing multiple samples of the relationship between functional and anatomical space. Both simulations and analyses of real fMRI data show that ASA improves the precision, objectivity and reproducibility of functional brain mapping.     

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.     

小波分析在层析图像重构中的应用研究

小波分析作为一种非平稳信号分析方法,具有良好的时（ 空）、频局部化特性和多分辨率特性。介绍了小波分析的基本原理和应用,引入小波分析进行图像重构,利用小波分解后得到的多分辨率的稀疏矩阵表示,设计了一迭代重构算法。通过计算机仿真试验,验证了小波分析在计算层析（ＣＴ） 成像光谱技术中能够应用于图像重构,并证实了小波分析的迭代重构算法是稳定、多分辨率和快速收敛的。     

基于支撑先验与深度图像先验的无预训练磁共振图像重建方法

基于深度学习的磁共振成像(magnetic resonance imaging, MRI)方法需要大规模、高质量的病患数据样本集进行预训练.然而,由于病患隐私及设备等因素限制,获取大规模、高质量的磁共振数据集在实际临床应用中面临挑战.本文提出一种新的基于深度学习的欠采样磁共振图像重建方法,该方法无需预训练、不依赖训练数据集,而是充分利用待重建的目标MR图像的结构先验和支撑先验,并将其引入深度图像先验(deep image prior, DIP)框架,从而削减对训练数据集的依赖,提升学习效率.基于参考图像与目标图像的相似性,采用高分辨率参考图像作为深度网络输入,将结构先验信息引入网络;将参考图像在小波域中幅值大的系数索引集作为目标图像的已知支撑集,构造正则化约束项,将网络训练转化为网络参数的最优化求解过程.实验结果表明,本文方法可由欠采样k空间数据重建得到更精确的磁共振图像,且在保留组织特征、细节纹理方面具有明显优势.     

Remote-sensing image encryption in hybrid domains

Remote-sensing technology plays an important role in military and industrial fields. Remote-sensing image is the main means of acquiring information from satellites, which always contain some confidential information. To securely transmit and store remote-sensing images, we propose a new image encryption algorithm in hybrid domains. This algorithm makes full use of the advantages of image encryption in both spatial domain and transform domain. First, the low-pass subband coefficients of image DWT (discrete wavelet transform) decomposition are sorted by a PWLCM system in transform domain. Second, the image after IDWT (inverse discrete wavelet transform) reconstruction is diffused with 2D (two-dimensional) Logistic map and XOR operation in spatial domain. The experiment results and algorithm analyses show that the new algorithm possesses a large key space and can resist brute-force, statistical and differential attacks. Meanwhile, the proposed algorithm has the desirable encryption efficiency to satisfy requirements in practice.     

基于结构字典学习的图像复原方法

本文提出一种新的结构字典学习方法,并利用它进行图像复原。首先给出结构字典学习的基本内容和方法,然后将傅里叶正则化方法和结构字典学习方法有效整合到图像复原算法中。结构字典学习方法是先将原图像进行结构分解,再分别学习出每个结构图像中的字典,最后利用这些字典对原图像进行稀疏的表示。结合傅里叶正则化,提出了一种有效的迭代图像复原算法:第一步在傅里叶域利用正则化反卷积方法得到图像的初步估计;第二步采用结构字典学习的方法对遗留的噪声进行去噪处理。实验结果表明,提出的方法在改进信噪比和视觉质量上都要优于6种先进的图像复原方法,改进的信噪比平均提升0.5 d B以上。     

Fast multi-contrast MRI reconstruction

Multi-contrast magnetic resonance imaging (MRI) is a useful technique to aid clinical diagnosis. This paper proposes an efficient algorithm to jointly reconstruct multiple T1/T2-weighted images of the same anatomical cross section from partially sampled k-space data. The joint reconstruction problem is formulated as minimizing a linear combination of three terms, corresponding to a least squares data fitting, joint total variation (TV) and group wavelet-sparsity regularization. It is rooted in two observations: 1) the variance of image gradients should be similar for the same spatial position across multiple contrasts; 2) the wavelet coefficients of all images from the same anatomical cross section should have similar sparse modes. To efficiently solve this problem, we decompose it into joint TV regularization and group sparsity subproblems, respectively. Finally, the reconstructed image is obtained from the weighted average of solutions from the two subproblems, in an iterative framework. Experiments demonstrate the efficiency and effectiveness of the proposed method compared to existing multi-contrast MRI methods.     

基于变分推断的磁共振图像群组配准

为解决基于深度学习的成对配准方法精度低和传统配准算法耗时长的问题,本文提出一种基于变分推断的无监督端到端的群组配准以及基于局部归一化互相关（NCC）和先验的配准框架,该框架能够将多个图像配准到公共空间并有效地控制变形场的正则化,且不需要真实的变形场和参考图像．该方法得到的预估变形场可建模为概率生成模型,使用变分推断的方法求解;然后借助空间转换网络和损失函数来实现无监督方式训练．对于公开数据集LPBA40的3D脑磁共振图像配准任务,测试结果表明：本文所提出的方法与基线方法相比,具有较好的Dice得分、运行时间少且产生更好的微分同胚域,同时对噪声具有鲁棒性．     

小波在求解黑体辐射反问题中的应用

针对黑体辐射反问题,提出将其离散为线性不适定问题,利用小波变换方法进行数值求解.将小波变换和正则化方法相结合,利用小波函数的紧支撑性,将原不适定问题转化为粗子空间上的适定问题.数值模拟结果表明方法可行,重构区域温度分布有效.     

Object extraction as a basic process for content-based image retrieval (CBIR) system

This article describes the way in which image is prepared for content-based image retrieval system. Automated image extraction is crucial; especially, if we take into consideration the fact that the feature selection is still a task performed by human domain experts and represents a major stumbling block in the process of creating fully autonomous CBIR systems. Our CBIR system is dedicated to support estate agents. In the database, there are images of houses and bungalows. We put all our efforts into extracting elements from an image and finding their characteristic features in the unsupervised way. Hence, the paper presents segmentation algorithm based on a pixel colour in RGB colour space. Next, it presents the method of object extraction applied to obtain separate objects prepared for the process of introducing them into database and further recognition. Moreover, we present a novel method of texture identification which is based on wavelet transformation. Due to the fact that the majority of texture is geometrical (such as bricks and tiles) we have used the Haar wavelet. After a set of low-level features for all objects is computed, the database is stored with these features.     

Wavelet-based edge correlation incorporated iterative reconstruction for undersampled MRI

Undersampling k-space is an effective way to decrease acquisition time for MRI. However, aliasing artifacts introduced by undersampling may blur the edges of magnetic resonance images, which often contain important information for clinical diagnosis. Moreover, k-space data is often contaminated by the noise signals of unknown intensity. To better preserve the edge features while suppressing the aliasing artifacts and noises, we present a new wavelet-based algorithm for undersampled MRI reconstruction. The algorithm solves the image reconstruction as a standard optimization problem including a ?₂ data fidelity term and ?₁ sparsity regularization term. Rather than manually setting the regularization parameter for the ?₁ term, which is directly related to the threshold, an automatic estimated threshold adaptive to noise intensity is introduced in our proposed algorithm. In addition, a prior matrix based on edge correlation in wavelet domain is incorporated into the regularization term. Compared with nonlinear conjugate gradient descent algorithm, iterative shrinkage/thresholding algorithm, fast iterative soft-thresholding algorithm and the iterative thresholding algorithm using exponentially decreasing threshold, the proposed algorithm yields reconstructions with better edge recovery and noise suppression.     

Optimization of hyperparameters for SMS reconstruction

PurposeSimultaneous multi-slice (SMS) imaging accelerates MRI data acquisition by exciting multiple image slices with a single radiofrequency pulse. Overlapping slices encoded in acquired signal are separated using a mathematical model, which requires estimation of image reconstruction kernels using calibration data. Several parameters used in SMS reconstruction impact the quality and fidelity of final images. Therefore, finding an optimal set of reconstruction parameters is critical to ensure that accelerated acquisition does not significantly degrade resulting image quality.MethodsGradient-echo echo planar imaging data were acquired with a range of SMS acceleration factors from a cohort of five volunteers with no known neurological pathology. Images were collected using two available phased-array head coils (a 48-channel array and a reduced diameter 32-channel array) that support SMS. Data from these coils were identically reconstructed offline using a range of coil compression factors and reconstruction kernel parameters. A hybrid space (k-x), externally-calibrated coil-by-coil slice unaliasing approach was used for image reconstruction. The image quality of the resulting reconstructed SMS images was assessed by evaluating correlations with identical echo-planar reference data acquired without SMS. A finger tapping functional MRI (fMRI) experiment was also performed and group analysis results were compared between data sets reconstructed with different coil compression levels.ResultsBetween the two RF coils tested in this study, the 32-channel coil with smaller dimensions clearly outperformed the larger 48-channel coil in our experiments. Generally, a large calibration region (144–192 samples) and small kernel sizes (2–4 samples) in k_y direction improved image quality. Use of regularization in the kernel fitting procedure had a notable impact on the fidelity of reconstructed images and a regularization value 0.0001 provided good image quality. With optimal selection of other hyperparameters in the hybrid space SMS unaliasing algorithm, coil compression caused small reduction in correlation between single-band and SMS unaliased images. Similarly, group analysis of fMRI results did not show a significant influence of coil compression on resulting image quality.ConclusionsThis study demonstrated that the hyperparameters used in SMS reconstruction need to be fine-tuned once the experimental factors such as the RF receive coil and SMS factor have been determined. A cursory evaluation of SMS reconstruction hyperparameter values is therefore recommended before conducting a full-scale quantitative study using SMS technologies.     

一种基于小波分析的小目标检测算法

红外小目标检测技术由于其重要的军事意义成为研究热点。根据目标、噪声和背景边缘在小波域的不同特点,提出一种基于小波分析的红外小目标检测算法。该算法利用小波对奇异信号强有力的分析能力,消除了噪声和背景边缘对小目标检测的干扰,实现目标的检出。仿真实验证明该方法对红外图像中的小目标有比较理想的检测效果。     

Sparsity driven ultrasound imaging

An image formation framework for ultrasound imaging from synthetic transducer arrays based on sparsity-driven regularization functionals using single-frequency Fourier domain data is proposed. The framework involves the use of a physics-based forward model of the ultrasound observation process, the formulation of image formation as the solution of an associated optimization problem, and the solution of that problem through efficient numerical algorithms. The sparsity-driven, model-based approach estimates a complex-valued reflectivity field and preserves physical features in the scene while suppressing spurious artifacts. It also provides robust reconstructions in the case of sparse and reduced observation apertures. The effectiveness of the proposed imaging strategy is demonstrated using experimental data.     

Synchronized detection of minute electrical currents with MRI using Lorentz effect imaging

The blood oxygenation level-dependent (BOLD) effect is the most commonly used contrast mechanism in functional magnetic resonance imaging (fMRI), due to its relatively high spatial resolution and sensitivity. However, the ability of BOLD fMRI to accurately localize neuronal activation in space and time is limited by the inherent hemodynamic modulation. There is hence a need to develop alternative MRI methods that can directly image neuroelectric activity, thereby achieving both a high temporal resolution and spatial specificity as compared to conventional BOLD fMRI. In this paper, we extend the Lorentz effect imaging technique, which can detect spatially incoherent yet temporally synchronized minute electrical activity in a strong magnetic field, and demonstrate its feasibility for imaging randomly oriented electrical currents on the order of microamperes with a temporal resolution on the order of milliseconds in gel phantoms. This constitutes a promising step towards its application to direct imaging of neuroelectric activity in vivo, which has the same order of current density and temporal synchrony.     

小波域内的盲水印提取

在对水印嵌入位的假设检验基础上，提出了一种盲水印的逐位提取模型，并在小波域得到了实现.为平衡水印的不可见性和鲁棒性，根据图像小波域的特征，并利用上下文建模的方法为每个高频小波系数确定不同的水印幅度，从而使水印的嵌入强度依图像的特征而变化.由于水印提取的结果在很大程度上依赖于图像小波系数的统计分布模型，因此小波域中的系数建模采用了广义高斯分布，并使用极大似然法估计参量.实验表明，该方法具有良好的鲁棒性.     

基于SPIHT的改进图像压缩算法

针对渐进式图像传输算法都受限于庞大的内存空间和计算复杂度，提出一种基于SPIHT的改进型算法——静止图像编码方法，即对变换后的小波系数高频区块进行细分，并对不同频率图像块分别设置阈值，采取新的阈值判别策略，减少了链表的结点数。使用MATLAB 6.5开发环境对上述改进编码方法进行仿真。仿真结果表明: 通过对原算法构架进行改进，减少了内存空间占用，降低了计算复杂度，取得了较好的压缩效果。     

Wavelet analysis and the geometry of Euclidean domains

This paper gives an explicit representation for a multiresolution of Euclidean domains and their boundaries in terms of a wavelet system defined in the ambient space. The exterior derivative of the characteristic function of a domain is represented in an infinite series of compactly supported wavelet functions whose supports intersect the geometric boundary. This is used to obtain representations of the boundary integrals which appear in weak solutions of partial differential equations.     

Compressed MRI reconstruction exploiting a rotation-invariant total variation discretization

Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereupon, the proposed MRI reconstruction model is presented as a constrained optimization problem, however, we do not use conventional ADMM-type algorithms designed for constrained problems to obtain a solution, but rather we tailor the linesearch-equipped method of Malitsky and Pock to our model, which was originally proposed for unconstrained problems. As attested by numerical experiments, this framework significantly outperforms various state-of-the-art algorithms from variational methods to adaptive and learning approaches and in particular, it eliminates the stagnating behavior of a previous work on BM3D-MRI which compromised the solution beyond a certain iteration.