Measurement of the point-spread function of a noisy imaging system

The averaged point-spread function (PSF) estimation of an image acquisition system is important for many computer vision applications, including edge detection and depth from defocus. The paper compares several mathematical models of the PSF and presents an improved measurement technique that enables subpixel estimation of 2D functions. New methods for noise suppression and uneven illumination modeling were incorporated. The PSF was computed from an ensemble of edge-spread function measurements. The generalized Gaussian was shown to be an 8 times better fit to the estimated PSF than the Gaussian and a 14 times better fit than the pillbox model.     

3D phase diversity: a myopic deconvolution method for short-exposure images: application to retinal imaging

3D deconvolution is an established technique in microscopy that may be useful for low-cost high-resolution imaging of the retina. We report on a myopic 3D deconvolution method developed in a Bayesian framework. This method uses a 3D imaging model, a noise model that accounts for both photon and detector noises, a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas, a positivity constraint, and a smart parameterization of the point-spread function (PSF) by the pupil phase. It estimates the object and the PSF jointly. The PSF parameterization through the pupil phase constrains the inversion by dramatically reducing the number of unknowns. The joint deconvolution is further constrained by an additional longitudinal support constraint derived from a 3D interpretation of the phase-diversity technique. This method is validated by simulated retinal images.     

Single-shot blind uniform motion deblurring with ringing reduction

In this paper, we have proposed a blind motion deblurring algorithm that comprises the estimation of the motion blur parameters (length and angle) in a modified cepstrum domain with a blind no-reference image spatial quality evaluator (BRISQUE) used for the tuning of point spread function (PSF) parameters. Ringing artifacts are generated during the deblurring process. In this paper, the modified R–L (Richardson–Lucy) algorithm with weight calculation based on graphcut is presented to obtain good estimates of the unblurred image with ringing reduction. The method involves the selection of different weights for edges and smooth regions such that the ringing effect over R–L iterations can be reduced. A newly proposed method has been tested on various natural images with a motion blur of different length and degrees. A comparison with state-of-the-art methods proves that the proposed technique achieved better results in terms of different quality measures such as SSIM, FSIM and PSNR and can be greatly beneficial for deblurring purpose.     

A fatigue model with local sensitivity analysis

The goal of this paper is two fold. First, it introduces a general parametric lifetime model for high‐cycle fatigue regime derived from physical, statistical, engineering and dimensional analysis considerations. The proposed model has two threshold parameters and three Weibull distribution parameters. A two‐step procedure is presented to estimate the parameters. In the first step, the two threshold parameters are estimated by minimizing a least squares regression function. In the second step, the parameters are estimated by the maximum likelihood method after pooling together the data from different stress levels. Since parameter estimation should always be accompanied by a sensitivity analysis of the fitted model, the second goal of this paper is to propose a method for sensitivity analysis for fatigue models. We show that the proposed sensitivity analysis methods are general and can be applied to any fatigue or lifetime model, not just to the one proposed here. Although several fatigue models have been proposed in the literature, to our knowledge this is the first attempt to produce methods for sensitivity analysis for fatigue models. The proposed method makes use of the well‐known duality property of mathematical programming, which states that the partial derivatives of the primal objective function with respect to the constraints right hand side parameters are the optimal values of the negative of the dual problem variables. For the parameters or data, for which sensitivities are sought, to appear on the right hand side, they are converted into artificial variables and set to their actual values, thus obtaining the desired constraints. Both the estimation and sensitivity analysis methods are illustrated by two examples, one application using real fatigue data and the other using simulated data. In addition, the sensitivity proposed method is also applied to an alternative fatigue model. Finally, some specific conclusions and recommendations are also given.     

MISTRAL: a myopic edge-preserving image restoration method, with application to astronomical adaptive-optics-corrected long-exposure images

Deconvolution is a necessary tool for the exploitation of a number of imaging instruments. We describe a deconvolution method developed in a Bayesian framework in the context of imaging through turbulence with adaptive optics. This method uses a noise model that accounts for both photonic and detector noises. It additionally contains a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas. Finally, it reckons with an imperfect knowledge of the point-spread function (PSF) by estimating the PSF jointly with the object under soft constraints rather than blindly (i.e., without constraints). These constraints are designed to embody our knowledge of the PSF. The implementation of this method is called MISTRAL. It is validated by simulations, and its effectiveness is illustrated by deconvolution results on experimental data taken on various adaptive optics systems and telescopes. Some of these deconvolutions have already been used to derive published astrophysical interpretations.     

Modeling the failure data of a repairable equipment with bathtub type failure intensity

The paper deals with the reliability modeling of the failure process of large and complex repairable equipment whose failure intensity shows a bathtub type non-monotonic behavior. A non-homogeneous Poisson process arising from the superposition of two power law processes is proposed, and the characteristics and mathematical details of the proposed model are illustrated. A graphical approach is also presented, which allows to determine whether the proposed model can adequately describe a given failure data. A graphical method for obtaining crude but easy estimates of the model parameters is then illustrated, as well as more accurate estimates based on the maximum likelihood method are provided. Finally, two numerical applications are given to illustrate the proposed model and the estimation procedures.     

Monte Carlo simulation of the atmospheric point-spread function with an application to correction for the adjacency effect

Monte Carlo techniques are used to simulate atmospheric point-spread functions (PSF's) that are appropriate for the viewing geometries typical of the Airborne Visible-Infrared Imaging Spectrometer (AVIRIS). A model sensor is located at an altitude of 20 km and views a Lambertian surface through a horizontally homogeneous and vertically stratified atmosphere. Simulations show the effects on the PSF of variation of the aerosol phase function, the aerosol optical thickness, the sensor viewing angle, and the wavelength. An algorithm that uses the PSF to correct high-contrast images for adjacency effects is developed and applied to an AVIRIS image of Big Pine Key in the Florida Keys. A method to approximate the atmospheric PSF's without the need to resort to a Monte Carlo simulation is described. Correction of the AVIRIS image through the use of the approximated PSF is consistent with a previous correction. Error analysis is difficult and scene dependent; however, the correction algorithm is shown to be capable of indicating regions of high-contrast images in which conventional estimates of surface-leaving radiance are likely to be unreliable due to adjacency effects.     

Conditional pairwise estimation in the Rasch model for ordered response categories using principal components

In the Rasch model for items with more than two ordered response categories, the thresholds that define the successive categories are an integral part of the structure of each item in that the probability of the response in any category is a function of all thresholds, not just the thresholds between any two categories. This paper describes a method of estimation for the Rasch model that takes advantage of this structure. In particular, instead of estimating the thresholds directly, it estimates the principal components of the thresholds, from which threshold estimates are then recovered. The principal components are estimated using a pairwise maximum likelihood algorithm which specialises to the well known algorithm for dichotomous items. The method of estimation has three advantageous properties. First, by considering items in all possible pairs, sufficiency in the Rasch model is exploited with the person parameter conditioned out in estimating the item parameters, and by analogy to the pairwise algorithm for dichotomous items, the estimates appear to be consistent, though unlike for the dichotomous case, no formal proof has yet been provided. Second, the estimates of each item parameter is a function of frequencies in all categories of the item rather than just a function of frequencies of two adjacent categories. This stabilizes estimates in the presence of low frequency data. Third, the procedure accounts readily for missing data. All of these properties are important when the model is used for constructing variables from large scale data sets which must account for structurally missing data. A simulation study shows that the quality of the estimates is excellent.     

4Pi microscopy deconvolution with a variable point-spread function

To remove the axial sidelobes from 4Pi images, deconvolution forms an integral part of 4Pi microscopy. As a result of its high axial resolution, the 4Pi point spread function (PSF) is particularly susceptible to imperfect optical conditions within the sample. This is typically observed as a shift in the position of the maxima under the PSF envelope. A significantly varying phase shift renders deconvolution procedures based on a spatially invariant PSF essentially useless. We present a technique for computing the forward transformation in the case of a varying phase at a computational expense of the same order of magnitude as that of the shift invariant case, a method for the estimation of PSF phase from an acquired image, and a deconvolution procedure built on these techniques.     

Measurement of in-plane and out-of-plane displacements and strains using digital holographic moiré

The paper proposes a non-destructive method for simultaneous measurement of in-plane and out-of-plane displacements and strains undergone by a deformed specimen from a single moiré fringe pattern obtained on the specimen in a dual beam digital holographic interferometry setup. The moiré fringe pattern encodes multiple interference phases which carry the information on multidimensional deformation. The interference field is segmented in each column and is modeled as multicomponent quadratic/cubic frequency-modulated signal in each segment. Subsequently, the product form of modified cubic phase function is used for accurate estimation of phase parameters. The estimated phase parameters are further utilized for direct estimation of the unwrapped interference phases and phase derivatives. The simulation and experimental results are provided to validate the effectiveness of the proposed method.     

Correction of dichroic mirror-induced PSF distortion in STED microscopy

Due to its spectral transmission/reflection properties, dichroic mirror (DM) is widely applied in nearly all microscopes to separate and combine beams with diverse wavelengths. However, its potential distortion effects to the point-spread function (PSF) have been ignored to a large extent. Here, we built a mathematical model to quantify these effects. Specifically, we focus on STED microscopy, whose performance is extremely sensitive to the systematic deficiencies. Both excitation and depletion beams are analysed, and the peak intensity and the shape of the effective PSF are calculated accordingly. More importantly, the strategy to compensate the DM-induced PSF distortion is also given in this paper.     

混响环境中突发声源定向方法及性能

针对突发性声源在混响条件下的定向技术进行了研究。基于传统广义互相关时延估计的定向方法,通过对互相关函数计算结果进行判别与约束、对数据帧采用滑动方式、对时延估计结果进行能量加权选举等措施,有效提高了声源定向结果的稳定性。实验结果表明,改进的算法在混响条件下能有效地对突发性声源进行可靠定向,可用于对枪声、爆炸声等突发性信号进行精确定向和定位。     

Parameter estimation of orthotropic plates by Bayesian sensitivity analysis

A method is developed to revise the elastic properties of a thin composite plate vibration model in an iterative manner such that its modified analytical responses eventually match those obtained experimentally. Once the revision process is completed, the resulting properties are considered the true properties of the plate and a non-destructive method for parameters evaluation is thus established. Formulation of a Rayleigh-Ritz model enables the calculation of the natural modes of vibration and an accurate finite element model is used to assess the confidence of these modes. Experimental modes as target responses are extracted by modal testing. Statistical Bayesian estimation is then applied to direct the adjustments of the parameters based on the discrepancies between the analytical and experimental responses. This method takes into account both the confidence associated with mathematical modelling and parameter estimates. Satisfactory convergence of the iteration scheme has been observed for several generally orthotropic glass/epoxy plates. Of all the constants determined using this approach, the elastic moduli are most accurate.     

Effects of a priori parameter selection in minimum relative entropy method on inverse electrocardiography problem

The goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface measurements and a mathematical model of torso–heart geometry that relates the sources to the measurements. This problem is ill-posed due to attenuation and smoothing that occur inside the thorax, and small errors in the measurements yield large reconstruction errors. To overcome this, ill-posedness, traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition and statistical approaches such as Bayesian Maximum A Posteriori estimation and Kalman filter have been applied. Statistical methods have yielded accurate inverse solutions; however, they require knowledge of a good a priori probability density function, or state transition definition. Minimum relative entropy (MRE) is an approach for inferring probability density function from a set of constraints and prior information, and may be an alternative to those statistical methods since it operates with more simple prior information definitions. However, success of the MRE method also depends on good choice of prior parameters in the form of upper and lower bound values, expected uncertainty in the model and the prior mean. In this paper, we explore the effects of each of these parameters on the solution of inverse ECG problem and discuss the limitations of the method. Our results show that the prior expected value is the most influential of the three MRE parameters.     

An Error-Minimizing Approach to Regularization in Indirect Measurements

Indirect measurements often amount to the estimation of the parameters of a mathematical model that describes the object under investigation, and this process may numerically be ill conditioned. Various regularization techniques are used to solve the problem. This paper shows that popular regularization methods can be depicted as special cases of a generalized approach based on a penalty term in the minimized criterion function and how different kinds of a priori knowledge can be engaged into each of them. A new function, which depends on the estimate bias and variance, is proposed to find a regularization parameter that minimizes the error of estimation, as well as a novel approach for nonlinear estimation that results in the iterative minimization (IM) method. The superiority of IM with respect to the conventional Marquardt procedure is demonstrated. Based on analysis, it also follows that the regularization technique can be used even in the case of numerically well-conditioned indirect measurements, decreasing the total error of estimation.      

Estimation of the parameters of one-dimensional maps from chaotic time series

The problem of constructing model maps based on the experimental chaotic time series is considered. A new method of estimation of the model parameters for one-dimensional maps is proposed, which employs a least squares procedure and calculations of the objective function using iterations of the model map in the reverse time. The results of a numerical experiment show that the proposed method provides much more accurate estimates than does the traditional approach at a moderate noise level below a certain threshold. The greater the number of parameters to be evaluated, the higher the threshold and, hence, the broader the domain of high efficiency of the new method.     

Accurate retrieval of region of interest for estimating point spread function and image deblurring

Extraction of an optimal region of interest (ROI) is crucial in many image processing applications, such as estimation of the point spread function (PSF) and blind deconvolution (BD). Although the amount of publications on PSF and BD is quite extensive; however, the work on ROI estimation has not received much attention. Existing methods which used heuristic models are not only time-consuming but also computationally expensive. In this paper, we proposed a new ROI retrieval scheme based on image partitioning and entropy measurement feedback. This method has low computation cost since it contains no matrix operations. Comprehensive experiments on real and synthetic datasets revealed that the proposed method is competitive when compared with existing search techniques, averaging at 26.1?dB, 0.46 and 1.44 on peak signal-to-noise ratio, universal image quality index and error ratio scales, respectively. On average, the proposed method takes less than 10?s to retrieve the ROI which is significantly faster compared to established solution.     

Amplitude-only versus amplitude-phase estimation

The feasibility of transfer function estimation based on amplitude-only measurements is verified. Its properties are compared to those of a full complex estimation using both the magnitude and the phase information of the estimated transfer function. The Fisher information matrix is used as a basis of comparison. It is found that the amplitude-only estimation has a larger standard deviation on the transfer function parameters. Optimal excitation for the analyzed examples is calculated for both methods. The main difference between them is that amplitude estimates require more energy further in the transition band. The variance of the amplitude estimates is highly dependent on the excitation bandwidth used. Care has to be taken to provide sufficient excitation in the transition band(s) of the device under test to obtain sensible results with amplitude estimates     

Estimation of point-spread functions and modulation-transfer functions of optical devices by statistical properties of randomly distributed surfaces

The point-spread function a(PSF) and the modulation-transfer function (MTF) are important tools to characterize the information transfer through optical devices. They give useful information about the resolution. Several methods have already been achieved to calculate the PSF and the MTF from theoretical aspects of wave propagation or from experimental results. I present a novel way of estimating these two functions. It deals with statistical considerations for a randomly distributed surface involving a statistical determination of the PSF and the MTF. Indeed, in this case the theoretical shape of the autocorrelation function of such surface profiles is known. It is a decaying exponential function α[exp(-β|x|)]. Comparingthe theoretical autocorrelation-function profile with the experimental one and deconvolving in Fourier space leads to an estimation of the MTF of the imaging device. Applying the inverse Fourier transform to the MTF involves the computation of the PSF, assuming that the latter has no imaginary part and is symmetrical. The two-dimensional images are regarded as an iteration of one-dimensional ones according to the orthogonal direction. The MTF's and PSF's are therefore one-dimensional. Different results are presented. The first result proceeds from investigation with scanning near-field microscopy and illustrates the method step by step. The tunneling effect is detected assuming that the information transfer is linear. The last result concerns an optical profilometer, and the influence of the microscope objective is studied.     

基于点扩散函数的散焦图像复原及其效果比较

针对已知的散焦图像数学模型,通过先估计点扩散函数(PSF),然后利用维纳滤波估计原始清晰图像的方法,探讨PSF、调制传递函数(MTF)的估计方法,具体包括边缘地物法、空间频率响应法、基于APEX方法的估计算法.结合复原图像的模糊度客观评价函数和主观视觉评价来判别各方法的优劣,结果表明:边缘地物法较优.