Multiframe blind deconvolution applied to diverse shift-and-add images of an astronomical object

In astronomical speckle imaging, deconvolving a shift-and-add (SAA) image has an advantage over deconvolving noisy specklegrams, because an SAA image is an integration of many specklegrams and has a relatively enhanced signal-tonoise ratio. In this paper, to reinforce the deconvolution of a single SAA image, we propose a multiframe deconvolution applied to multiple SAA images that are obtained by diversely recombining the same set of specklegrams to have different point spread functions. We have found that such diverse SAA images can be easily produced by permuting specklegrams to be processed by SAA. The results of experiments using simulated and observational data have shown a robustness of our present approach: in the previous approach of deconvolving a single SAA frame, the resulting object estimate is apt to be influenced by the given SAA frame and the estimation sometimes fails, whereas in the present approach, a reliable object image is stably reconstructed regardless of the given SAA frames.     

4Pi confocal microscopy with alternate interference

We introduce 4Pi confocal microscopy with destructive interference of converging waves. Linear lobe deconvolution as well as nonlinear restoration of 4Pi confocal raw data with their point-spread functions (PSF's) leads to almost-identical images, irrespective of whether the 4Pi confocal PSF relies on constructive or destructive interference. Three-dimensional imaging of microtubules of a mouse fibroblast cell yielded an axial resolution near 100-nm in both cases. Moreover, restoration of 4Pi confocal images of the same object with alternate phases is introduced as a powerful test for (nonlinear) image restoration.     

Blind image deconvolution using the zero-lag slice of higher-order statistics

A novel algorithm for blind image deconvolution using the zero-lag slice (ZLS) of higher-order statistics only is presented. This method first estimates the point-spread function (PSF) using the ZLS of its third-order moment (TOM) and then uses it with one of the known classical image deconvolution methods. The proposed method has simple computations for PSF estimation because it solves a nonlinear problem by using an iterative method with fast convergence. In each iteration, one need only calculate the ZLS of the TOM and estimate the PSF using simple two-dimensional operations. Furthermore, the method presented achieves good results, since the ZLS estimate obtained from the degraded image exhibits high reliability. The good performance of the proposed algorithm is demonstrated by applying it to synthetic and real data sets.     

Gradient-Based Blind Deconvolution with Phase Spectral Constraints

This paper proposes a new blind deconvolution method with additional phase spectral constraints for a blurred image. A degradation of an original image is mathematically modeled by a convolution of an original image and a point-spread function (PSF). The proposed method consists of the following three steps: (i) projection onto a complex set satisfying the phase spectral constraint in a frequency space; (ii) minimization of a cost function preserving the constrained phase spectra; and (iii) projection onto an image space satisfying nonnegative and support constraints. This method restores both the original image and the PSF with high accuracy. The effectiveness of the proposed method is verified by applying it to some blind deconvolution problems for digital images, and the experimental results show that the performance is superior to the conventional blind deconvolution methods.     

Mobile gravitoinertial system based on the three-component method of inertial navigation

A model of a ballistically unperturbed (stable) gravimetric system is suggested, the functioning of which is based on conversion of inertial information and (radial) position information about the object’s motion.     

A simplified approach for the generation of projection data for cone beam geometry

To test a developed reconstruction algorithm for cone beam geometry, whether it is transmission or emission tomography, one needs projection data. Generally, mathematical phantoms are generated in three dimensions and the projection for all rotation angles is calculated. For non-symmetric objects, the process is cumbersome and computation intensive. This paper describes a simple methodology for the generation of projection data for cone beam geometry for both transmission and emission tomographies by knowing the object’s attenuation and/or source spatial distribution details as input. The object details such as internal geometrical distribution are nowhere involved in the projection data calculation. This simple approach uses the pixilated object matrix values in terms of the matrix indices and spatial geometrical coordinates. The projection data of some typical phantoms (generated using this approach) are reconstructed using standard FDK algorithm and Novikov’s inversion formula. Correlation between the original and reconstructed images has been calculated to compare the image quality.     

利用维纳滤波改善声透镜光声成像系统的分辨率

为了克服衍射效应对光声成像系统分辨率的限制,需要采用逆卷积方法进行图像反演.从理论上分析了声透镜成像原理,模拟仿真了声透镜的点扩展函数对声透镜成像系统分辨率的影响和维纳滤波解卷积方法复原光声成像的过程,并利用自搭建的声透镜光声成像系统进行了深入的实验研究,得到了物平面上相距4 mm和3 mm的两个黑胶带点的直接成像光声...     

Application of multi-frame approach in single-frame blind deconvolution

A new single-frame blind deconvolution algorithm for the linear shift-invariant imaging system is presented. The algorithm processes the partial images segmented from one single degraded image by multi-frame approach to recover the point spread function (PSF). Then a deconvolution method is employed to restore the whole image with the recovered PSF. In addition, in order to improve the fidelity and resolution of the recovered PSF, the coprimeness of the partial images is utilized. Results of simulated and real atmospheric turbulence degraded images using the algorithm are reported.     

自适应光学图像非对称图像迭代盲复原算法

 为了提高自适应光学图像复原效果,提出了一种新的多重约束非对称图像迭代盲解卷积算法。首先,在点扩散函数（PSF）频率域引入带宽有限约束来提高迭代盲解卷积算法的可靠性;然后,在PSF空间域引入支持域动态更新的思想以加快迭代盲解卷积算法收敛速度;最后,自动计算迭代盲解卷积算法的非对称因子以提高算法的自适应性。模拟实验结果表明,与RL-IBD算法比较,新算法迭代次数减少22.4%、峰值信噪比提高10.18 dB。在FK5-857和某双星的自适应光学图像复原实验中,也取得很好的复原效果。     

基于目标和点扩展函数联合估计的点源目标图像近视解卷积

在传统的基于波前探测的解卷积方法中,由波前探测得到的点扩展函数被认为是精确的,并用维纳滤波进行复原,但是点扩展函数不可避免地存在误差,所以最终的复原目标图像质量不佳.为了解决该难题,提出了基于目标和点扩展函数联合估计的图像近视解卷积算法.它运用了点扩展函数和目标的先验信息,对点扩展函数和目标进行了规整和进一步约束,从而得到更优的恢复图像质量.对该方法的原理和实现过程进行了阐述,并将其运用于室内点源目标数据中.实验结果证明,与维纳滤波方法相比,该方法使图像恢复的效果得到明显改善.     

Super-resolution by pupil plane phase filtering

Resolution capability of any optical imaging system is limited by residual aberrations as well as diffraction effects. Overcoming this fundamental limit is called super-resolution. Several new paradigms for super-resolution in optical systems use ‘a posteriori’ digital image processing. In these ventures the three-dimensional point spread function (PSF) of the lens plays a key role in image acquisition. A straightforward tailoring of the PSF can be performed by appropriate pupil plane filtering. With a brief review of the state-of-art in this research area, this paper dwells upon the inverse problem of global optimization of the pupil function by phase filtering in accordance with the desired PSF.     

Static point-spread function correction dominating higher-order speckle terms at high adaptive correction

At high adaptive correction, the randomly shifting speckles familiar in conventional astronomical imaging become organized into patterns with distinct regularities that may permit partial suppression of the image noise they produce. Mathematically, the phase exponential in the Fourier-optical imaging expression may be expanded in a Taylor series in remnant phase phi, which is small at very high correction, leading to a perturbed point-spread function (PSF) that is a sum of algebraic terms, each of distinct spatial symmetry. At sufficiently high correction, one need deal with only a few of the lowest-order terms. A first-order expansion gives an ideal PSF plus two terms, linear and quadratic, describing the two brightest, physically most relevant kinds of speckle. A second-order expansion gives three new terms, the brightest of which is primarily a static correction to the PSF, with a much smaller true speckle component. When the correction is great enough to isolate individual speckle terms, the two terms from the first-order expansion alone determine the essential physics. A general observational strategy is outlined for reducing speckle noise in highly corrected companion searches, dominated by a few speckle terms of definite spatial symmetry.     

A two-stage method to correct aberrations induced by slide slant in bright-field microscopy

To achieve optimal image quality in bright field microscopy, the slide surface should be perpendicular to the optical axis of the microscope. However, in the recently proposed “slanted scan” slide acquisition technique, scan speed is increased by purposely slanting the slide by a small angle (of 3–5°) so that multiple focal depths can be imaged simultaneously. In this case, the slanted slide introduces a bend in the point spread function (PSF), resulting in a coma and other aberrations that degrade image quality. In this paper, we propose a two-stage deconvolution method specifically designed to correct the aberrations induced by a slanted scan, but with general applicability to high-resolution bright-field microscopy. Specifically, we initially apply phase deconvolution to correct the dominating coma aberration, before applying a conventional semi-blind deconvolution method to further improve image resolution and contrast. We also propose a novel method to estimate the degree of coma aberration and the PSF of the optics utilising actual cytology specimens. The efficacy of the proposed algorithm is demonstrated quantitatively on simulated data, against a ground-truth (object) image, and qualitatively on cervical cytology specimens. Results demonstrate both improved convergence speed of the two-stage approach, especially when correcting the bend in the PSF, and a resultant image quality that is comparable to a conventionally (flat) scanned specimen.     

Self-deconvolution for shift-and-add imaging

A shift-and-add (SAA) method is used to restore atmospherically degraded images. The operation of the SAA method is simple, but the deconvolution method of SAA images remains to be developed, especially for extended objects. We propose to deconvolve a SAA image of an extended object by use of a self-deconvolving data reconstruction algorithm (SeDDaRA). Computer simulations show the effectiveness of the SeDDaRA to SAA images. It is also shown that use of the SAA method after each data frame is self-deconvolved leads to a better reconstruction.     

谱域光学相干层析系统中基于解卷积方法的像质优化

谱域光学相干层析（spectral domain optical coherence tomography, 简记为SD-OCT）系统的轴向点扩散函数（point spread function, 简记为PSF）并不具备空不变特性,无法直接应用于解卷积运算.为实现SD-OCT系统成像质量基于解卷积算法的优化,本文采用数值校正后的轴向扫描信号和轴向有效PSF来实施基于Lucy-Richardson算法的解卷积运算,进而实现了SD-OCT系统中图像质量尤其是轴向分辨率的改善.本文理论分析了SD-OCT系统中导致轴向有效PSF随成像深度增大而下降和图像模糊的因素,阐述了利用解卷积算法实现图像质量优化的过程,基于建立的SD-OCT系统实施了不同成像深度位置处PSF的标定,并利用离散轴向位置处PSF的峰值拟合了轴向有效PSF的调制函数.利用调制函数对所有轴向扫描信号进行数值校正,然后根据轴向有效PSF进行解卷积算法.典型样品的解卷积图像重建结果表明,提出的解卷积方法能有效提高系统的轴向分辨率,同时有效抑制系统灵敏度随成像深度增大而下降的趋势. 关键词： 谱域光学相干层析 Lucy-Richardson解卷积 有效点扩散函数     

谱域光学相干层析系统中基于解卷积方法的像质优化

谱域光学相干层析（spectral domain optical coherence tomography, 简记为SD-OCT）系统的轴向点扩散函数（point spread function, 简记为PSF）并不具备空不变特性,无法直接应用于解卷积运算.为实现SD-OCT系统成像质量基于解卷积算法的优化,本文采用数值校正后的轴向扫描信号和轴向有效PSF来实施基于Lucy-Richardson算法的解卷积运算,进而实现了SD-OCT系统中图像质量尤其是轴向分辨率的改善.本文理论分析了SD-OCT系统中导致轴向有效PSF随成像深度增大而下降和图像模糊的因素,阐述了利用解卷积算法实现图像质量优化的过程,基于建立的SD-OCT系统实施了不同成像深度位置处PSF的标定,并利用离散轴向位置处PSF的峰值拟合了轴向有效PSF的调制函数.利用调制函数对所有轴向扫描信号进行数值校正,然后根据轴向有效PSF进行解卷积算法.典型样品的解卷积图像重建结果表明,提出的解卷积方法能有效提高系统的轴向分辨率,同时有效抑制系统灵敏度随成像深度增大而下降的趋势.     

Polarization difference image analysis with LC filter

Image analysis using polarizing methods allows removing the polarized light component from recorded images. This is known as polarization difference imaging (PDI). The use of liquid crystals (LC) in PDI was proposed in 2002. Modified LC unit with a properly oriented LC layer was proposed by the authors. The main parameters which characterize an imaging system, employing a circular LC filter, were determined and presented in previous papers. In this work, the basics of the circular LC filter construction and theory are presented. Two application configurations of PDI imaging systems are shown. Experimental results of image processing based on object’s polarization properties are discussed.     

三维显微图像复原及点扩散函数的研究

三维显微图像去卷积计算量巨大,运算时间长。评价和分析了三维点扩散函数、散焦像、光学切片以及不同三维点扩散函数去卷积的复原图像,进一步证明了散焦光信息对焦面像的干扰,主要来自于焦面像两侧附近的散焦像。提出了折中选择三维PSF的空间大小,可以获得良好的复原效果,并且减少运行时间。提出了频谱图均值的新概念,作为评价图像清晰及模糊程度的标准,并运用于散焦像、光学切片以及复原结果图的评价。     

Single image motion deblurring: An accurate PSF estimation and ringing reduction

In this paper we have proposed a single image motion deblurring algorithm that is based on a novel use of dual Fourier spectrum combined with bit plane slicing algorithm and Radon transform (RT) for accurate estimation of PSF parameters such as, blur length and blur angle. Even after very accurate PSF estimation, the deconvolution algorithms tend to introduce ringing artifacts at boundaries and near strong edges. To prevent this post deconvolution effect, a post processing method is also proposed in the framework of traditional Richardson–Lucy (RL) deconvolution algorithm. Experimental results evaluated on the basis of both qualitative and quantitative (PSNR, SSIM) metrics, verified on the dataset of both grayscale and color blurred images show that the proposed method outperforms the existing algorithms for removal of uniform blur. A comparison with state-of-the-art methods proves the usefulness of the proposed algorithm for deblurring real-life images/photographs.