Correction of aeroheating-induced intensity nonuniformity in infrared images

Aeroheating-induced intensity nonuniformity effects severely influence the effective performance of an infrared (IR) imaging system in high-speed flight. In this paper, we propose a new approach to the correction of intensity nonuniformity in IR images. The basic assumption is that the low-frequency intensity bias is additive and smoothly varying so that it can be modeled as a bivariate polynomial and estimated by using an isotropic total variation (TV) model. A half quadratic penalty method is applied to the isotropic form of TV discretization. And an alternating minimization algorithm is adopted for solving the optimization model. The experimental results of simulated and real aerothermal images show that the proposed correction method can effectively improve IR image quality.     

Holographic display based on compressive sensing (Invited Paper)

We propose a method to improve the quality of the reconstructed images based on compressive sensing principles. The pseudo-inverse matrix and the total variation minimization algorithms are combined to reduce the sampling number of the computer generated hologram. Numerical simulations are performed and the results indicate that the peak signal to noise ratio is increased and the sampling ratio is decreased at the same time for holographic display.     

基于Cycle Spinning Contourlet变换和总变分最小化的遥感图像去噪算法

针对很多已有的遥感图像去噪算法去噪的同时存在不能有效的保留细节和增强边缘的问题,提出了一种基于Cycle Spinning Contourlet变换和总变分最小化的图像去噪新算法。该算法依据了Cycle Spinning Contourlet变换能够很好的保留原始图像的细节和纹理信息,而总变分最小化方法具有在去噪的同时增强图像边缘的特性,因此使用所提出的融合规则对两种算法去噪后的图像进行融合能够取得更好的增强效果。通过对比,实验结果表明该算法不仅能在很大程度上削弱分别由平移不变Contourlet变换和总变分最小化的图像去噪方法产生的伪吉布斯现象和阶梯效应,而且视觉效果和PSNR值均优于其它方法,同时该算法能够保留更多的光谱信息,因此该算法是一种有效的遥感图像去噪算法。     

基于Cycle Spinning Contourlet变换和总变分最小化的遥感图像去噪算法(英文)

针对大部分已有的遥感图像去噪算法在去噪的同时不能有效的保留细节和增强边缘,提出了一种基于Cycle Spinning Contourlet变换和总变分最小化的图像去噪新算法.该算法依据了Cycle Spinning Contourlet变换能够很好的保留原始图像的细节和纹理信息,而总变分最小化方法具有在去噪的同时增强图像边缘的特性,因此使用所提出的融合规则对两种算法去噪后的图像进行融合能够取得更好的增强效果.通过对比,实验结果表明该算法不仅能在很大程度上削弱分别由平移不变Contourlet变换和总变分最小化的图像去噪方法产生的伪吉布斯现象和阶梯效应,而且视觉效果和PSNR值均优于其它方法,同时该算法能够保留更多的光谱信息,因此该算法是一种有效的遥感图像去噪算法.     

Multiframe blind image deconvolution with split Bregman method

In the paper, a multiframe blind image deconvolution method based on total variation and framelet regularizer is proposed. An adapted version of the split Bregman method is proposed to efficiently solve the resulting minimization problems. In each iteration, four sub-problems need to be solved, one of which can be very efficiently and easily solved via fast Fourier transform implementation or closed form solution. Both simulated noisy and blurred frames and real degraded frames are used to verify the effectiveness of the proposed method. Comparative experimental results show that the proposed method can efficiently remove the blur and noises and restore high quality sharp image.     

A Compton scattering image reconstruction algorithm based on total variation minimization

Compton scattering imaging is a novel radiation imaging method using scattered photons.Its main characteristics are detectors that do not have to be on the opposite side of the source,so avoiding the rotation process.The reconstruction problem of Compton scattering imaging is the inverse problem to solve electron densities from nonlinear equations,which is ill-posed.This means the solution exhibits instability and sensitivity to noise or erroneous measurements.Using the theory for reconstruction of sparse images,a reconstruction algorithm based on total variation minimization is proposed.The reconstruction problem is described as an optimization problem with nonlinear data-consistency constraint.The simulated results show that the proposed algorithm could reduce reconstruction error and improve image quality,especially when there are not enough measurements.     

Blind image deconvolution subject to bandwidth and total variation constraints

We present a maximum likelihood (ML) deconvolution algorithm with bandwidth and total variation (TV) constraints for degraded image due to atmospheric turbulence. The bandwidth limit function is estimated in view of optical system parameters and Fourier optical theory. With the aid of bandwidth and TV minimization as compelling constraints, the algorithm can not only suppress noise effectively but also restrict the bandwidth of point-spread function (PSF) that may lead to trivial solution. Compared with the conventional ML method, the proposed algorithm is able to restore a noise-free image, and the detailed texture is better than that of ML.     

Color image edge detection method using VTV denoising and color difference

The traditional Canny edge uses Gaussian filter to suppress the noise, it also smoothes out the image edges. An improved Canny edge detection method for color image is proposed in this paper, the improved method uses fast vectorial total variation (VTV) minimization model to remove noise in color image, and then calculates the color difference and direction in CIELAB color space, which is used for non-maximal suppression. Finally, the improved method extracts the edges by the double-threshold method. The experimental results show that the proposed method achieves better performance than the traditional Canny edge detector. It can remove noise while preserving the image edges, and effectively detect the image edges.     

Sixth moment optimization of multi-channel Bragg filters

The design of multichannel optical filter is studied theoretically. New efficient two-step method based on combination of 6-th moment minimization and straightforward numerical minimization is developed. It is applied to find a fiber Bragg grating profile with minimal refractive index variation for 5 ÷ 32 channels. Obtained results are closer to the theoretical limit than previously reported.     

Local diffusion regularization method for optical tomography reconstruction by using robust statistics

We formulate a solution to the diffuse optical tomography (DOT) inverse problem as the minimization of an energy functional of the solution and the data. For the solution prior we introduce a local diffusion regularization potential with a threshold based on robust statistics (the Hubert function). We compare results on simulated data for the Hubert function and two other standard regularization functionals, Tikhonov and total variation.     

基于全变分最小化和交替方向法的康普顿散射成像重建算法

康普顿散射成像技术利用射线与物质作用后的散射光子信息对物质的电子密度进行成像.与传统的透射成像方式相比,康普顿散射成像具有系统结构灵活、成像对比度高、辐射剂量低等优势,在无损检测、医疗诊断、安全检查等领域有着广阔的应用前景.但其重建问题是一个非线性的逆问题,通常是不适定的,其解对噪声和测量误差非常敏感.为解决此问题,本文结合全变分最小化正则化方法和交替方向法提出了一种新的康普顿散射成像重建算法.该算法首先将问题对应的TV模型转化为与之等价的带约束的优化问题,然后利用增广拉格朗日乘子法将优化问题分解为两个具有解析解的子问题,并通过交替求解子问题使增广拉格朗日函数达到最小,进而得到重建的图像.在仿真实验中,通过与主流的ASD-POCS方法进行对比,证明了该算法在重建精度和重建效率方面的优势.     

德拜色散媒质的三维时域电磁逆散射技术

生物组织、土壤、水等媒质的电特性是频率相关的(称为色散媒质),常利用单极德拜(Debye)模型描述.为重建这一类媒质的色散特性,基于泛函分析和变分法,提出一种三维(3-D)时域电磁(EM)逆散射技术,主要流程为:①根据最小二乘准则,转化逆散射问题为约束最小化问题;②应用罚函数法,转化约束最小化问题为无约束最小化问题;③通过变分计算,解析导出梯度(Fréchet导数)表达式;④利用梯度法求解.此外,引入一阶吉洪诺夫(Tikhonov)正则化以应对逆问题的病态特性和噪声影响.数值应用中,将提出的目的 应用到一个简单的三维癌变乳房模型,借助PRP共轭梯度(CG)算法和时域有限差分(FDTD)法,仿真结果初步证实本文目的 的可行性、有效性和鲁棒性.     

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.     

Structure of Flux Line Lattices in Tilt Magnetic Fields of Anisotropic Superconductos

We study here, by the minimization of the total energy of flux line systems, the zero temperature structure of flux lines of uniaxial anisotropic superconductors in a tilt magnetic field. The anisotropic London model is used and an efficient method is developed to make the total energy calculation manageable. Two degenerate structures are found, one is a deformed triangular structure and the other is a superlattice with three lines per unit cell.     

非精确交替方向总变分最小化重建算法

CT (computed tomography)系统实际应用当中, 经常会出现扫描数据不满足数据完备性条件的情况. 针对不完全角度重建问题的研究, 是目前迭代型算法研究中的一个热点. 一系列基于带有约束的总变分最小化的重建算法近年来在不完全角度重建中取得了较好的效果, 这其中基于交替方向法 (alternating direction method, ADM) 的重建算法表现出更好的性能. 然而, ADM方法在求解过程中对矩阵求逆的处理效率不高, 导致极大的计算开销. 本文针对该问题, 使用非精确ADM方法, 利用线性近似的方式替换掉计算开销较大的项, 使得矩阵求逆问题可以通过快速傅里叶变换加速实现. 实验结果表明, 本文提出的非精确交替方向总变分最小化重建算法与精确ADM重建算法相比, 没有明显的精度损失, 计算时间缩减30%左右. 关键词： 不完全角度重建 总变分最小化 非精确交替方向法     

Reconstruction of dynamic displacement and velocity from measured accelerations using the variational statement of an inverse problem

This paper presents two types of finite impulse response (FIR) filters to reconstruct dynamic displacement induced by structural vibration from measured acceleration. The governing equation for the reconstruction is derived by taking the variation of a minimization problem, which defines an inverse problem on displacement. A regularization function for overcoming the ill-posedness of the inverse problem is included in the minimization problem. The governing equation of the inverse problem becomes the same type of differential equation as that of a beam on an elastic foundation. The conventional FIR (CFIR) filter directly approximates the transfer function of the governing equation, while the FEM-based FIR (FFIR) filter is formulated by the discretization of the minimization problem with the finite element method. For the finite element discretization, the Hermitian shape function is utilized. The proposed FFIR filter is capable of reconstructing displacement and velocity simultaneously. The fundamental characteristics of the proposed filters are investigated in the frequency domain using the transfer and accuracy functions. It is shown that the proposed FIR filters suppress low frequency noise components in measured accelerations effectively, and reconstruct physically meaningful displacement accurately. The validity of the proposed filters is demonstrated through a numerical simulation study, a field experiment and an evaluation of flutter derivatives using measurements taken from a wind tunnel test.     

Damage and fracture evolution in brittle materials by shape optimization methods

This paper is devoted to a numerical implementation of the Francfort–Marigo model of damage evolution in brittle materials. This quasi-static model is based, at each time step, on the minimization of a total energy which is the sum of an elastic energy and a Griffith-type dissipated energy. Such a minimization is carried over all geometric mixtures of the two, healthy and damaged, elastic phases, respecting an irreversibility constraint. Numerically, we consider a situation where two well-separated phases coexist, and model their interface by a level set function that is transported according to the shape derivative of the minimized total energy. In the context of interface variations (Hadamard method) and using a steepest descent algorithm, we compute local minimizers of this quasi-static damage model. Initially, the damaged zone is nucleated by using the so-called topological derivative. We show that, when the damaged phase is very weak, our numerical method is able to predict crack propagation, including kinking and branching. Several numerical examples in 2d and 3d are discussed.     

High-speed video capture by a single flutter shutter camera using three-dimensional hyperbolic wavelets

Based on the consideration of easy achievement in modern sensors, this paper further exploits the possibility of the recovery of high-speed video (HSV) by a single flutter shutter camera. Taking into account different degrees of smoothness along the spatial and temporal dimensions of HSV, this paper proposes to use a three-dimensional hyperbolic wavelet basis based on Kronecker product to jointly model the spatial and temporal redundancy of HSV. Besides, we incorporate the total variation of temporal correlations in HSV as a prior knowledge to further enhance our reconstruction quality. We recover the underlying HSV frames from the observed low-speed coded video by solving a convex minimization problem. The experimental results on simulated and real-world videos both demonstrate the validity of the proposed method.     

基于广义变分正则化的闪光照相图像重建算法

 针对闪光照相图像信噪比低的特点,提出了一种基于广义变分正则化的图像重建算法,该方法采用p-范数取代目前广泛采用的全变分范数作为正则项,构造了用于图像重建的展平泛函,将图像重建问题转化为目标泛函最优化问题,采用固定点迭代法求解图像重建的最优解。数值计算结果表明,该算法在重建过程中能够有效抑制图像噪声,并加大对图像边缘的保持能力,从而提高了图像重建质量,是一种有效且性能优良的闪光照相图像重建算法。     

Optimization of STEM-HAADF Electron Tomography Reconstructions by Parameter Selection in Compressed Sensing Total Variation Minimization-Based Algorithms

A novel procedure to optimize the 3D morphological characterization of nanomaterials by means of high angle annular dark field scanning-transmission electron tomography is reported and is successfully applied to the analysis of a metal- and halogen-free ordered mesoporous carbon material. The new method is based on a selection of the two parameters (μ and β) which are key in the reconstruction of tomographic series by means of total variation minimization (TVM). The parameter-selected TVM reconstructions obtained using this approach clearly reveal the porous structure of the carbon-based material as consisting of a network of parallel, straight channels of ≈6 nm diameter ordered in a honeycomb-type arrangement. Such an unusual structure cannot be retrieved from a TVM 3D reconstruction using default reconstruction values. Moreover, segmentation and further quantification of the optimized 3D tomographic reconstruction provide values for different textural parameters, such as pore size distribution and specific pore volume that match very closely with those determined by macroscopic physisorption techniques. The approach developed can be extended to other reconstruction models in which the final result is influenced by parameter choice.