Optimum spatial filter for image restoration degraded by multiplicative noise

We discuss the problem of image restoration when the image is degraded by multiplicative noise. In order to solve this problem, we use as a criterion the minimization of the mean-square error between the restored and the original image. The transfer function of the optimum filter derived in this paper is described by the product of the conjugate of the transfer function of the imaging system and the power spectrum density of the degraded image divided by the convolution of the power spectrum density of the image and that of the noise. Some special cases of the filter are discussed. A numerical experiment has been performed and satisfactory results have been obtained.     

大口径干涉仪系统传递函数的修正和校准

 采用子孔径拼接法对传统系统传递函数校准方法进行修正。将大口径干涉仪视场分成若干个等晕区,采用标准台阶相位比较法分别测得每个等晕区的传递函数,然后将大口径干涉仪系统传递函数修正为每个等晕区传递函数的加权平均,其权重因子由对应等晕区内测试面的功率谱决定。实验结果表明:中心视场对应传递函数和修正后的系统传递函数在3 mm^-1附近处差值大于0.2;修正后的系统传递函数校准方法能更准确地得到波前功率谱密度。     

Blind deconvolution of audio-frequency signals using the self-deconvolving data restoration algorithm

A signal processing algorithm has been developed in which a filter function is extracted from degraded data through mathematical operations. The filter function can be used to restore much of the degraded content of the data through use of a deconvolution process. The operation can be performed without prior knowledge of the detection system, a technique known as blind deconvolution. The extraction process, designated self-deconvolving data reconstruction algorithm, is applied here to audio-frequency signals showing significant qualitative improvement. Degradation arising from the process of electronic recording and reproduction is significantly reduced.     

Gram-Charlier matched filter for Shack-Hartmann sensing at low light levels

A study has been made of a Gram-Charlier matched filter for Shack-Hartmann sensing of wave-front slopes. The method is based on modeling the point-spread function by an expansion in terms of Gauss-Hermite polynomials. We present results for several subapertureycoherence area sizes both with and without CCD read noise. A more accurate estimation of the local slopes can be achieved at low light levels in this way than with the standard first-moment estimator.     

Blur identification and restoration of degraded images using generalized cross-validation criterion

In this paper, we describe blur identification and restoration of noisy degraded images. The point-spread function (PSF) can be characterized by the quantity of blur. Thus the blur identification problem can be solved as a parameter estimation problem. The estimation method is a generalized cross-validation (GCV) criterion that is known as a powerful measure that can be used to choose the optimal regularization parameter without a priori knowledge about noise. We use the iterative damped-1east squares (DLS) algorithm which is based on the principle of damped least-squares for restoring noisy degraded images.     

基于BP神经网络的闪光照相图像复原

针对闪光照相系统模糊较大、成像信噪比较低的问题,提出了一种基于BP神经网络的闪光照相图像复原方法。该方法利用BP神经网络的泛化能力,用样本图像对网络进行训练,建立退化图像与真实图像之间的非线性映射关系,然后将待复原图像分区,利用训练好的BP神经网络对待复原图像的边界区域进行复原处理。数值试验表明,在系统点扩展函数未知的情况下,该算法能较好再现图像边缘信息,复原出的图像在信噪比和视觉方面都有较大提高。     

Optimized pupil-plane filters for confocal microscope point-spread function engineering

We present a new method of superresolving pupil-plane filter design in confocal microscopy in which we specify the properties of the desired point-spread function and use an optimization procedure to determine a suitable pupil-plane filter. A new, flexible method of filter implementation using reconfigurable binary optical elements is described, and experimental results are presented.     

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.     

Optical transfer functions of 4Pi confocal microscopes: theory and experiment

We measure the point-spread function in the two main configurations of 4Pi confocal microscopy as well as in the traditional confocal arrangement and derive the optical transfer functions from the experimental data. The optical transfer functions are in good agreement with their theoretical counterparts. We find a 3.5- to 5-fold increased axial bandwidth of the 4Pi confocal microscope and hence confirm the enhanced spatial-frequency content of 4Pi images.     

Sensitivity to point-spread function parameters in medical ultrasound image deconvolution

Clinical ultrasound images are often perceived as difficult to interpret due to image blurring and speckle inherent in the ultrasound imaging. But the image quality can be improved by deconvolution using an estimate of the point-spread function. However, it is difficult to obtain a sufficiently accurate estimate of the point-spread function in vivo because of the unknown properties of the soft tissue in clinical applications. Local variations in the speed of sound and attenuation change the pulse and beam shape. These in turn affect the point-spread function. The purpose and novelty of this paper is therefore to explore the sensitivity of a state-of-the-art deconvolution algorithm to uncertainty in the point-spread function. The point-spread function in our restoration algorithm is made shift invariant in the lateral dimension but shift dependent in the axial direction, and is modelled to match a 128-element 1D linear array often found in clinical use. We present simulated and in vitro sensitivity analyses of two-dimensional deconvolution while varying six parameters on which the point-spread function depends. Uncertainty in the ultrasound machine is analysed by varying the axial depths of lateral and elevational foci alongside height and width of transducer elements. Sensitivity to tissue influence is investigated by varying the speed of sound and frequency-dependent attenuation of the electro-mechanical impulse response. The results are analysed both quantitatively and in terms of the perceived image quality. First, the assessment of deconvolution using the logarithmic image amplitude is found to be a better indicator of the perceived improvement in the restoration. Secondly, the two most critical parameters for two-dimensional deconvolution are discovered to be the lateral focus and the speed of sound, because the success of deconvolution is perceived primarily in terms of deblurring. We also observed similar patterns for the simulation and in vitro experiment. Finally, we show that it is possible to restore in vivo ultrasound images using an assumed point-spread function and hence conclude that an exact point-spread function is not necessary for enhancing ultrasound image quality by deconvolution.     

滤光片型近红外仪器模型传递的研究

模型传递问题是近红外光谱分析技术中解决数据通用性的关键问题。文章以玉米籽粒近红外光谱图(检测其中水分含量)为例,考察了模型传递的问题。使用斜率截距算法,直接校正法和目标因子分析等算法,在5台滤光片型近红外仪器上实现了模型传递,并比较了各种方法的模型传递效果。研究表明,直接校正法的模型传递效果最好,4台从仪器的平均传递差异度为7.01%。文章还研究了标准样品数量对模型传递效果的影响。作为转换集的标准样品数目越多,模型传递效果越好,一般有20个标准样品就能达到稳定的效果。当转换集小于20时,直接校正法的传递效果急剧下降,而标准样品数量对斜率截距法和目标因子分析法的影响不明显。     

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.     

Lateral resolution enhancement with standing evanescent waves

A high-resolution fluorescence microscopy technique has been developed that achieves a lateral resolution of better than one sixth of the emission wavelength (FWHM). By use of a total-internal-reflection geometry, standing evanescent waves are generated that spatially modulate the excitation of the sample. An enhanced two-dimensional image is formed from a weighted sum of images taken at different phases and directions of the standing wave. The performance of such a system is examined through theoretical calculations of both the point-spread function and the optical transfer function.     

Improving image quality and T(1) measurements using saturation recovery turboFLASH with an approximate K-space normalisation filter

We present a method for reducing the image point-spread function and measuring T(1) using saturation recovery turboFLASH (SRTF) with centric-ordered k-space and a k-space correction filter designed to compensate for longitudinal magnetisation evolution during image acquisition. The method provides a two point T(1) measurement that reduces inaccuracies and image artefacts caused by longitudinal magnetisation evolution in conventional turboFLASH methods. The method is designed for use in rapid, quantitative measurements of contrast agent uptake in vivo.     

One-dimensional iterative algorithm for three-dimensional point-spread function engineering

We present a new method with which to binarize pupil filters designed to control the three-dimensional irradiance distribution in the focal volume of an optical system. The method is based on a one-dimensional iterative algorithm, which results in efficient use of computation time and in simple, easy to fabricate binary filters. An acceptable degree of resemblance between the point-spread function of the annular binary filter and that of its gray-tone counterpart is obtained.     

基于CCD尺寸测量中图像边缘退化及恢复技术研究

针对直边衍射效应造成的图像边缘退化问题,建立边缘退化模型。从菲涅尔直边衍射理论出发,基于信号与系统理论的图像边缘退化数学描述方法,分析了造成图像边缘退化的原因。通过分析不同光源波长和成像物距下直边衍射强度分布曲线的特点,构造简单函数实现衍射光强分布的近似,进而得到退化系统传递函数;利用退化系统传递函数构造滤波器对获取图像的边缘进行恢复,从而提高尺寸测量精度。实验结果表明:经边缘恢复方法校正后的测量结果误差约为0.02 mm,相对未校正数据的测量结果误差减小0.04 mm,提高了尺寸测量精度。     

Restoring parts of scenes from blurred photographs

Digital restorations are reported of parts of scenes photographed so badly out of focus that essential details in the scene are unrecognisable. The photographs are taken with a standard 35 mm camera using ordinary film. The part of the degraded image of interest is preprocessed by first compensating (on the basis of the known development time) for the gamma of the film and then applying our (recently reported) edge extension method. The out of focus point-spread function is determined experimentally and the final restoration is obtained by Wiener filtering. The blurred and restored versions of the number plate of a vehicle are presented.     

General IIR optical notch filter based on Michelson Gires–Tournois interferometer

A general IIR optical notch filter design is presented from a digital filter design perspective for Michelson Gires–Tournois Interferometer structure. Optical notch filter with arbitrary notch frequency, notch point number, and 3 dB rejection bandwidth can be designed easily. According to the spectral requirement of desired notch filter, in frequency domain we firstly calculate the transfer function of desired allpass filter. Then the numbers of reflectors in Gires–Tournois etalon can be determined. We calculate the transfer function of this multi-cavity Gires–Tournois etalon by using Z-transform. By making the transfer function of allpass filter in frequency domain equal to that of the multi-cavity Gires–Tournois etalon, the notch filter can be directly realized. Different design examples are given in detail in the paper. The change of output spectrum is also investigated for the reflectance of the reflectors and the distance between the reflectors deviating from the ideal value. The results show that the notch filter has the tunability of notch frequency and 3 dB rejection bandwidth. The chromatic dispersion characteristic of the notch filter is analyzed finally. It shows that the notch filter has excellent chromatic dispersion characteristic.     

Blind deconvolution under band limitation

A blind deconvolution problem is newly stated with the following conditions: the point-spread function is band limited, both the object and the point-spread function are nonnegative, and the solution is to be a diffraction-limited object. A blind deconvolution method was developed that can easily be applied to problems in optics because of the conditions used. The performance of the method is investigated with computer simulations.