改进的傅里叶域小波域联合去模糊算法

傅里叶域与小波域的联合去模糊算法在低噪声时具有优越的恢复效果,但是这种联合去模糊算法并不适用于含噪声的模糊图像.为了解决这一问题,本文将先验约束分别引入傅里叶域的去模糊步骤和小波域的去噪步骤.在傅里叶域,用矩阵形式表示目标函数.对目标函数添加平滑约束并且通过噪声水平和模糊图像高频信息计算得到平滑约束项的滤波系数.同样方式,在小波域对小波域目标函数添加能量约束,实现小波域目标函数的正则化过程.分析傅里叶域的噪声放大程度,通过傅里叶域的滤波系数计算得到小波域能量约束的滤波系数.傅里叶域的平滑约束可以抑制滤波过程中噪声的产生,小波域的能量约束可以提高小波域滤波的鲁棒性.仿真实验表明,改进的算法相比于原始算法具有更好的鲁棒性,可以有效提高图像的恢复质量.对于噪声标准差为0.010.1的模糊图像,改进算法恢复图像峰值信噪比比原始算法恢复图像的峰值信噪比高1左右.并且改进算法对于高斯型点扩散函数误差具有鲁棒性,当点扩散函数估计方差与实际方差相差0.4时,改进算法的恢复效果仍优于原始算法.     

High resolution optical image restoration for ground-based large telescope using phase diversity speckle

Phase diversity speckle (PDS) is an image restoration technique which is based on the idea of phase diversity (PD). It uses multi-frame short-exposure image sequence to calculate their corresponding wave-front information. Each image pair consists of two images collected by two cameras at the same time with one in focus and the other with known defocus value. Multi-frame processing can significantly improve the target signal to noise ratio, and decrease noise influence. In this paper, based on the principle of pupil Fourier imaging, by adjusting the pupil size, we get different scales of the optical point spread function (PSF). Also, we analysis different camera noise distribution channels, location differences and other factors to optimize the objective evaluation function, and this can reduce the computational complexity and improve the processing speed of image restoration. In the indoor environment, we build optical platform, and use multi-frame phase diversity speckle to make experiment under different turbulence conditions. The experimental results show that the image restoration effect of the proposed method is close to the diffraction limit.     

Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval

We propose a method to encrypt two covert images into an overt image based on phase-truncated Fourier transforms and phase retrieval. In this method, the two original images are self-encoded in the manner that one of the two images is directly separated into two phase masks (PMs) and used as keys for encryption, and then multiplied by a PM which is generated by using phase retrieval algorithm. At last, the whole encryption process is completed by a Fourier transform operation. In the decryption process, the image without a separation and the two PMs used as keys for encryption are all treated as encoded data. The cryptosystem is asymmetric which means the keys for encryption are different from those for decryption. Numerical simulations are presented to show the viability and good performance of the proposed method.     

基于频谱分析的匀速运动模糊图像模糊方向识别

点扩展函数的设置是图像复原中的关键问题，对于匀速直线运动模糊图像，运动方向和模糊长度决定了点扩展函数。根据运动模糊图像和原始图像在频谱上存在的对应关系，即运动模糊图像频谱存在着对应于传递函数零点的暗条纹，提出对运动模糊图像，通过二维傅里叶变换、二值化以及Radon变换检测运动模糊图像频谱图上暗条纹的方向和位置，来实现运动方向测量的方法。用该方法对模糊图像进行检测，模糊方向的识别精度小于1°。实验证明该方法可以实现平面内任意方向运动的测量。     

Blind restoration of real turbulence-degraded image with complicated backgrounds using anisotropic regularization

This paper proposes a novel blind image restoration method based on estimating the point-spread functions by using two real turbulence-degraded images as input. The non-negative constraint and the spatial correlation are transformed mathematically into the penalty terms and added to the objective function. An anisotropic and nonlinear regularization function is proposed to adequately punish the differences of the point spread functions (PSFs) in the process of optimization estimation. Some definitions of weighted second-order differences are given and a fast method to construct the matrix of second-order weighted gradient operator is derived. The PSF values can be quickly estimated. With the estimated PSFs, the true images can be recovered by non-blind restoration methods. Experiment results for the restoration of real turbulence-degraded images with complicated backgrounds support the effectiveness of this proposed method.     

Solving the problem of concomitant gradients in ultra-low-field MRI

In ultra-low-field magnetic resonance imaging (ULF MRI), spin precession is detected typically in magnetic fields of the order of 10-100 μT. As in conventional high-field MRI, the spatial origin of the signals can be encoded by superposing gradient fields on a homogeneous main field. However, because the main field is weak, gradient field amplitudes become comparable to it. In this case, the concomitant gradients forced by Maxwell's equations cause the assumption of linearly varying field gradients to fail. Thus, image reconstruction with Fourier transformation would produce severe image artifacts. We propose a direct linear inversion (DLI) method to reconstruct images without limiting assumptions about the gradient fields. We compare the quality of the images obtained using the proposed reconstruction method and the Fourier reconstruction. With simulations, we show how the reconstruction errors of the methods depend on the strengths of the concomitant gradients. The proposed approach produces nearly distortion-free images even when the main field reaches zero.     

Asymmetric multiple-image hiding using phase retrieval technique based on amplitude- and phase-truncation in fractional Fourier domain

We propose a multiple-image hiding scheme based on the amplitude- and phase-truncation approach, and phase retrieval iterative algorithm in the fractional Fourier domain. The proposed scheme offers multiple levels of security with asymmetric keys. Multiple input images multiplied with random phase masks are independently fractional Fourier transformed with different orders. The individual keys and common keys are generated by using phase and amplitude truncation of fractional spectrum. After using two fractional Fourier transform, the resultant encrypted image is hided in a host image with phase retrieval iterative algorithm. Using the correct universal keys, individual keys, and fractional orders, one can recover the original image successfully. Computer simulation results with four gray-scale images support the proposed method. To measure the validity of the scheme, we calculated the mean square error between the original and the decrypted images. In this scheme, the encryption process and generation of decryption keys are complicated and should be realized using computer. For decryption, an optoelectronic setup has been suggested.     

Reflexion of a spherical wave by the plane interface between a perfect fluid and a porous medium

By using the Fourier transform of the system of equations and continuity conditions, it is easy to obtain the Fourier transform of the solution. This last function is decomposed into several terms which are identified as Fourier images of known functions. An exact representation of the scattered sound pressure field is obtained as a combination of the radiation of the image source and layer potentials. Approximations are given when the point spherical source is located on the interface.     

基于多通道盲识别的自适应光学图像事后处理

为实时恢复天文或空间目标的湍流退化成像,提出一种适应大气湍流动态变化的多通道自适应光学图像恢复方法.以自适应光学校正后不同时刻的目标成像作为多个通道,建立求解系统点扩散函数的线性方程,根据解出的点扩散函数利用超拉普拉斯算法,求解待观测目标的估计值.结果表明:不同时刻的点扩散函数之间存在互质关系,满足多通道盲识别的理论要求.利用建立的线性方程求解出的点扩散函数与原点扩散函数的均方误差在10^-30~10^-27量级,采用超拉普拉斯算法恢复出的目标成像与原始目标之间的均方误差在10^-5~10^-4量级.本文研究为湍流退化图像的实时恢复提供了理论基础.     

Extraction of difference of two images using periodic carrier modulation

The optical method of extraction of difference between transparencies using periodic carrier modulation was first proposed and successfully demonstrated by Pennington. His method was based on the modulation of each of the image transparencies by the same grating with the difference that one modulating carrier was shifted by half-period with respect to the other. In order to ensure extraction of difference signal from unwanted sum signal, the modulating carrier frequency must be too low. This poses a serious problem because shifting a high frequency grating exactly by a half-period is not an easy task. In order to surmount this difficulty Belvaux and Lowenthal proposed that instead of using a grating, the images transparencies can be modulated by fringes obtained in a Wollaston prism. It is well-known that these fringes can be shifted by a half-period by rotating an analyzer at the output side by 90°. The optical methods of subtraction of images suffer from the disadvantage that the photographic record has to be developed and fixed by wet processes. The processed record is then Fourier transformed and suitably filtered to extract the difference signal. In the present paper we have carried out extraction of difference of two images using the principle of periodic carrier modulation by carrying out spatial frequency filtering of the total irradiance distribution numerically. Some of the results of subtraction are presented.