Performance of a phase-transformed input joint transform correlator

Conventionally a detected image is represented by an intensity array owing to the square-law nature of most detectors. However, this does not mean that we have to restrict ourselves to using intensity images for the correlation process. Transforming intensity images into phase images before correlation, which can be easily realized by a phase-modulation spatial light modulator, offers an alternative approach for high-performance pattern recognition. A phase-transformed input joint transform correlator is investigated in detail in terms of pattern discriminability, detection efficiency, and noise robustness. We show that the phase-transformed joint transform correlator has higher pattern discriminability and detection efficiency than the conventional joint transform correlator, and it also offers a better trade-off between the pattern discriminability and noise tolerance. A proof-of-concept experiment is also provided.     

Target segmentation in active polarimetric images by use of statistical active contours

We address the problem of target segmentation in active polarimetric images, which can reveal contrasts that do not appear in standard intensity images. However, these images are perturbed by strong specklelike noise. For the purpose of segmentation we thus use statistical active contours, which are known to possess noise robustness properties. The polarimetric imagers we consider acquire two different images of the same scene so as to form a two-channel image (TCI). These two images can be combined to form the orthogonal state contrast image (OSCI), which represents the degree of polarization of the backscattered light if its coherency matrix is diagonal. We characterize the segmentation performance of the statistical active contour procedure on the TCI and on the OSCI. In particular, we show that if the illumination beam is spatially nonuniform, it is more efficient to perform the segmentation on the OSCI, which is independent of the spatial variations of the illumination.     

Estimation of the degree of polarization in active coherent imagery by using the natural representation

We address the problem of degree of polarization estimation in polarization diversity images. We consider active imaging techniques with laser illumination, which have the appealing feature of revealing contrasts that do not appear in conventional intensity images. These techniques provide two images of the same scene that are perturbed with speckle noise. Because of the presence of nonhomogeneity in the reflected intensity, it can be preferable to perform image analysis of the orthogonal-state contrast image, which is a measure of the degree of polarization of the reflected light when the coherency matrix is diagonal. It has been shown that a simple nonlinear transformation of this orthogonal-state contrast image leads to an image perturbed with additive symmetrical noise on which simple and efficient estimation and detection techniques can be applied. We propose to precisely analyze estimation properties of the degree of polarization using this natural representation. In particular, we determine the Cramer-Rao bound of the polarization degree estimation and the variance of the proposed estimator, and we study the estimator's efficiency as a function of the speckle order for different measurement strategies.     

Reduction of speckle in digital holography by discrete Fourier filtering

We present a digital signal processing technique that reduces the speckle content in reconstructed digital holograms. The method is based on sequential sampling of the discrete Fourier transform of the reconstructed image field. Speckle reduction is achieved at the expense of a reduced intensity and resolution, but this trade-off is shown to be greatly superior to that imposed by the traditional mean and median filtering techniques. In particular, we show that the speckle can be reduced by half with no loss of resolution (according to standard definitions of both metrics).     

Quantitative temporal speckle contrast imaging for tissue mechanics

We demonstrate through a series of simulations that by parameterizing the temporal speckle contrast statistic from a sequence of translating speckle images on a number of experimental constants, the local temporal contrast can be used to quantitatively assess local motion, provided that the spatial and temporal Nyquist sampling criteria are both met. We develop a simple exponential model for quantifying speckle motion for speckle patterns that display arbitrary intensity statistics and provide suggestions for optimizing both the experimental acquisition of speckle data and the temporal contrast analysis of the data. The confounding effects of uncorrelated noise are also discussed. The model is demonstrated by applying it to an optical coherence tomography image sequence of an engineered tissue construct undergoing dynamic compression. Applications to tissue mechanics are shown, although the discussion is equally relevant for fluid motion studies.     

Balancing interpixel cross talk and detector noise to optimize areal density in holographic storage systems

We investigate the effects of interpixel cross talk and detector noise on the areal storage density of holographic data storage. A numerical simulation is used to obtain the bit-error rate (BER) as a function of hologram aperture, pixel fill factors, and additive Gaussian intensity noise. We consider the effect of interpixel cross talk at an output pixel from all possible configurations of its 12 closest-neighbor pixels. Experimental verification of this simulation procedure is shown for several fill-factor combinations. The simulation results show that areal density is maximized when the aperture coincides with the zero order of the spatial light modulator (SLM) (Nyquist sampling condition) and the CCD fill factor is large. Additional numerical analysis including finite SLM contrast and fixed-pattern noise show that, if the fixed-pattern noise reaches 6% of the mean signal level, the SLM contrast has to be larger than 6:1 to maintain high areal density. We also investigate the improvement of areal density when error-prone pixel combinations are forbidden by using coding schemes. A trade-off between an increase in areal density and the redundancy of a coding scheme that avoids isolated-on pixels occurs at a code rate of approximately 83%.     

Spectral optimized asymmetric segmented phase-only correlation filter

We suggest a new type of optimized composite filter, i.e., the asymmetric segmented phase-only filter (ASPOF), for improving the effectiveness of a VanderLugt correlator (VLC) when used for face identification. Basically, it consists in merging several reference images after application of a specific spectral optimization method. After segmentation of the spectral filter plane to several areas, each area is assigned to a single winner reference according to a new optimized criterion. The point of the paper is to show that this method offers a significant performance improvement on standard composite filters for face identification. We first briefly revisit composite filters [adapted, phase-only, inverse, compromise optimal, segmented, minimum average correlation energy, optimal trade-off maximum average correlation, and amplitude-modulated phase-only (AMPOF)], which are tools of choice for face recognition based on correlation techniques, and compare their performances with those of the ASPOF. We illustrate some of the drawbacks of current filters for several binary and grayscale image identifications. Next, we describe the optimization steps and introduce the ASPOF that can overcome these technical issues to improve the quality and the reliability of the correlation-based decision. We derive performance measures, i.e., PCE values and receiver operating characteristic curves, to confirm consistency of the results. We numerically find that this filter increases the recognition rate and decreases the false alarm rate. The results show that the discrimination of the ASPOF is comparable to that of the AMPOF, but the ASPOF is more robust than the trade-off maximum average correlation height against rotation and various types of noise sources. Our method has several features that make it amenable to experimental implementation using a VLC.     

Quantization noise and its reduction in lensless Fourier digital holography

Digital holography is an imaging technique that enables recovery of topographic 3D information about an object under investigation. In digital holography, an interference pattern is recorded on a digital camera. Therefore, quantization of the recorded hologram is an integral part of the imaging process. We study the influence of quantization error in the recorded holograms on the fidelity of both the intensity and phase of the reconstructed image. We limit our analysis to the case of lensless Fourier off-axis digital holograms. We derive a theoretical model to predict the effect of quantization noise and we validate this model using experimental results. Based on this, we also show how the resultant noise in the reconstructed image, as well as the speckle that is inherent in digital holography, can be conveniently suppressed by standard speckle reduction techniques. We show that high-quality images can be obtained from binary holograms when speckle reduction is performed.     

Estimates of the information content and dimensionality of natural scenes from proximity distributions

Natural scenes, like most all natural data sets, show considerable redundancy. Although many forms of redundancy have been investigated (e.g., pixel distributions, power spectra, contour relationships, etc.), estimates of the true entropy of natural scenes have been largely considered intractable. We describe a technique for estimating the entropy and relative dimensionality of image patches based on a function we call the proximity distribution (a nearest-neighbor technique). The advantage of this function over simple statistics such as the power spectrum is that the proximity distribution is dependent on all forms of redundancy. We demonstrate that this function can be used to estimate the entropy (redundancy) of 3x3 patches of known entropy as well as 8x8 patches of Gaussian white noise, natural scenes, and noise with the same power spectrum as natural scenes. The techniques are based on assumptions regarding the intrinsic dimensionality of the data, and although the estimates depend on an extrapolation model for images larger than 3x3, we argue that this approach provides the best current estimates of the entropy and compressibility of natural-scene patches and that it provides insights into the efficiency of any coding strategy that aims to reduce redundancy. We show that the sample of 8x8 patches of natural scenes used in this study has less than half the entropy of 8x8 white noise and less than 60% of the entropy of noise with the same power spectrum. In addition, given a finite number of samples (<2(20)) drawn randomly from the space of 8x8 patches, the subspace of 8x8 natural-scene patches shows a dimensionality that depends on the sampling density and that for low densities is significantly lower dimensional than the space of 8x8 patches of white noise and noise with the same power spectrum.     

Zero-order noise suppression with various space-shifting manipulations of reconstructed images in digital holography

In this paper, we describe various numerical space-shifting manipulations of the reconstructed images to remove the dc noise in the reconstruction, in terms of the periodicity characteristics of images in digital holography. The theoretical interpretation on different reconstruction periods of the image and the dc noise is described in detail for the first time, to the best of our knowledge. It is related to CCD sampling periods or frequencies for the fringes and the dc term of a hologram. With the calculations of Hadamard product of two different spatially shifted images and subsequent extraction of the root of it, the dc noise can be suppressed effectively and a clear image with the original intensity contrast can be obtained at the center in the hologram reconstruction, particularly when the image and the dc noise are completely or partially superposed with each other. The experiments for both in-line and off-axis imaging cases show that all results are completely consistent with theoretical predictions.     

基于多向投影新方法的捆钞印章个数统计

提出了一种快速自动统计印章个数的多向投影新方法。该方法基于图像处理理论,将采集到的捆钞图像从RGB空间转为LUV空间,然后通过聚类分析算法,得到捆钞的二值化图像,再利用多向投影的思路,依次在垂直和水平方向投影变换,完成印章个数的统计。理论分析及实验结果表明,该方法可以有效去除背景噪声的影响,不依赖于印章印迹的好坏,提高了印章个数自动统计的效率和准确率。     

Broadband volume holographic imaging

We demonstrate transmission geometry volume holograms working under broadband illumination. We show that increased illumination bandwidth enhances the lateral field of view of planar reference holograms. We exploit this phenomenon to design volume holographic spectrum analyzers and present results from an experimental prototype. Furthermore, we show that there is a trade-off involved, because an improvement in the field of view results in a reduction of image contrast as a function of depth. We experimentally demonstrate this trade-off and discuss possible ways to overcome it.     

Wavelet tests for the detection of transients in the VIRGO interferometric gravitational wave detector

Here we employ discrete wavelet transforms (DWTs) to develop test statistics for the detection of transients, i.e., signals with a short duration and unknown shape, embedded in Gaussian white noise. Distributions of the test statistics under both the and alternative hypotheses can be easily derived. We test performance on a set of 78 templates provided by theoretical studies on gravitational waves emitted in a supernova explosion where we seek the maximal detection distance of the source generating the signal at which the tests correctly reject the hypothesis. We discuss practical implementation issues and performance assessment methods. We compare results with both matched filtering, an optimal method that requires the prior knowledge of the signal shape, and with the slope filtering, that uses limited prior knowledge on the signal. The wavelet statistics show a good behavior for each of the considered waveforms, unlike other detection methods.     

Robust trade-off portfolio selection

Robust portfolio selection explicitly incorporates a model of parameter uncertainty in the problem formulation, and optimizes for the worst-case scenario. We consider robust mean–variance portfolio selection involving a trade-off between the worst-case utility and the worst-case regret, or the largest difference between the best utility achievable under the model and that achieved by a given portfolio. While optimizing for the worst-case utility may yield an overly pessimistic portfolio, optimizing for the worst-case regret may result in a complete loss of robustness; we theoretically demonstrate this point. Robust trade-off portfolio compromises these two extremes, enabling more informative selections. We show that, under a widely used ellipsoidal uncertainty model, the entire optimal trade-off curve can be found via solving a series of semidefinite programs (SDPs). We then extend the model to handle the union of finitely many ellipsoids, and show that trade-off analysis under this quite general uncertainty model also reduces to a series of SDPs. For more general uncertainties, we propose an iterative algorithm based on the cutting-set method. Under the finite-union-of-ellipsoids model, this algorithm offers an alternative to the SDP in exploring the optimal trade-off curve. We illustrate the promises of the trade-off portfolios by using historical stock returns data.

     

Optimal multichannel estimation of the location of a target with nonoverlapping noise

We propose a new algorithm for estimating the location of an object in multichannel images when the noise is spatially disjointed from (nonoverlapping with) the target. This algorithm is optimal for nonoverlapping noise and for multichannel images in the maximum-likelihood sense. We consider the case in which the statistical parameters of the input scene are unknown and are estimated by observation. We assess the results for simulated images with white and Gaussian background, for a large scale of variances of the background noise, and different values of the contrast in the scene. We compare the results of this algorithm with the results obtained with two other algorithms, the optimal algorithm for monochannel nonoverlapping noise and the optimal algorithm for multichannel additive noise, and we show that in both cases improvement can be obtained. We show the efficiency of the estimation for real input scenes when the background noise is correlated clutter noise. This algorithm has the same complexity as correlation, and the improvement is obtained with no more calculation cost than with classic methods.     

Polarization imaging by use of digital holography

We present what we believe to be a new digital holographic imaging method that is able to determine simultaneously the distributions of intensity, phase, and polarization state at the surface of a specimen on the basis of a single image acquisition. Two reference waves with orthogonal polarization states interfere with the object wave to create a hologram that is recorded on a CCD camera. Two wave fronts, one for each perpendicular polarization state, are numerically reconstructed in intensity and phase. Combining the intensity and the phase distributions of these two wave fronts permits the determination of all the components of the Jones vector of the object-wave front. We show that this method can be used to image and measure the distribution of the polarization state at the surface of a specimen, and the obtained results indicate that precise quantitative measurements of the polarization state can be achieved. An application of the method to image the birefringence of a stressed polymethyl methacrylate sample is presented.     

Measuring phase shifts and energy dissipation with amplitude modulation atomic force microscopy

By recording the phase angle difference between the excitation force and the tip response in amplitude modulation AFM it is possible to image compositional variations in heterogeneous samples. In this contribution we address some of the experimental issues relevant to perform phase contrast imaging measurements. Specifically, we study the dependence of the phase shift on the tip-surface separation, interaction regime, cantilever parameters, free amplitude and tip-surface dissipative processes. We show that phase shift measurements can be converted into energy dissipation values. Energy dissipation curves show a maximum (～10?eV/cycle) with the amplitude ratio. Furthermore, energy dissipation maps provide a robust method to image material properties because they do not depend directly on the tip-surface interaction regime. Compositional contrast images are illustrated by imaging conjugated molecular islands deposited on silicon surfaces.     

Maximum likelihood for target location in the presence of substitutive noise

We consider the optimal likelihood algorithm for the estimation of a target location when the images are corrupted by substitutive noise. We show the relationship between the optimal algorithm and the sliced orthogonal nonlinear generalized (SONG) correlation. The SONG correlation is based on the application of a linear correlation to corresponding binary slices of both the input scene and the reference object with appropriate weight factors. For a particular case, we show that the optimal strategy is a function of only the number of pixels for which the gray values in the noisy image match the ones of the reference image when the substitutive noise is uniformly distributed. This is exactly what a particular definition of the SONG correlation does.     

Statistics of the contrast of coherent images

Contrast optimization, also known as image sharpening, is a method that can be used to estimate phase errors in coherent images. However, the contrast measure of a coherent image is a random variable because of the speckle present in coherent images. The variance of this measure puts a limit on the ability of contrast optimization to focus an image. We derive the probability distribution function of the most common contrast measure, the sum of the pixel intensities raised to a power. These statistics are then verified by a number of speckle simulations and compared with measured statistics from synthetic aperture sonar images. The developed statistics can be used as a tool to understand and improve the method of contrast optimization as well as assess its performance for a given imaging system. They can also be used to predict the effect of certain image processing operations on the contrast.     

Generalized cross-validation as a stopping rule for the Richardson-Lucy algorithm

The Richardson-Lucy (R-L) algorithm has been widely used to restore degraded astronomical images. This algorithm is nothing more than the expectation-maximization (EM) algorithm applied to Poisson data. The R-L method is iterative in nature and converges to a (possibly local) maximum of the likelihood function. Unfortunately, because of the ill-conditioned nature of the problem, this maximum likelihood estimate may actually be a very poor restoration. One way to prevent degradation of the restoration is to stop the iteration before it reaches convergence. A number of methods have been proposed for determining the optimal stopping point-the point that provides the best trade-off between restoring the image and amplifying the noise. Cross-validation (CV) has recently been proposed as an advantageous method for determining the optimal stopping point. We propose a different form of CV based on generalized cross-validation (GCV) that overcomes some of the difficulties of CV. We derive a GCV-based criterion for the R-L algorithm that can be efficiently evaluated at each iteration. We present examples displaying the power of the stopping rule and discuss the abilities and shortcomings of the method.