Proceedings Volume 3170

Image Reconstruction and Restoration II

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Proceedings Volume 3170

Image Reconstruction and Restoration II

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Volume Details

Date Published: 31 October 1997
Contents: 5 Sessions, 25 Papers, 0 Presentations
Conference: Optical Science, Engineering and Instrumentation '97 1997
Volume Number: 3170

Table of Contents

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Table of Contents

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  • Imaging Methods for Space Surveillance and Astronomy
  • Phase Retrieval
  • Remote Sensing Applications
  • Image Deblurring and Superresolution
  • Computed Tomography
  • Remote Sensing Applications
Imaging Methods for Space Surveillance and Astronomy
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Space object identification using phase-diverse speckle
John H. Seldin, Michael F. Reiley, Richard G. Paxman, et al.
Space-object identification from ground-based telescopes is challenging because of the degradation in resolution arising from atmospheric turbulence. Phase-diverse speckle is a novel post-detection correction method that can be used to overcome turbulence-induced aberrations for telescopes with or without adaptive optics. We present a simulation study of phase-diverse speckle satellite reconstructions for the Air Force Maui Optical station 1.6-meter telescope. For a given turbulence strength, satellite reconstruction fidelity is evaluated as a function of quality and quantity of data. The credibility of this study is enhanced by reconstructions from actual compensated data collected wit the 1.5-meter telescope at the Starfire Optical Range. Consistent details observed across a time series of reconstructions from a portion of a satellite pass enhance the authenticity of these features. We conclude that phase-diverse speckle can restore fine-resolution features not apparent in the raw aberrated images of space objects.
Expectation maximization approach to deconvolution from wavefront sensing
Experimental measurements and computer simulations show that the range of applicability of deconvolution from wavefront sensing can be extended by an expectation maximization approach.
Reconstruction of turbulence-degraded images using the vector Wiener filter
Stephen D. Ford, Byron M. Welsh, Michael C. Roggemann
Adaptive optics and speckle imaging are common methods for improving Fourier domain signal-to-noise ratio (SNR) in astronomical images. These techniques may benefit from linear processing to deconvolve blurring due to the attenuation of high spatial frequencies in the compensated images. Typical linear deconvolution methods require an explicit estimate of the random atmospheric-optical system point spread function or optical transfer function (OTF). In addition, a priori knowledge of the object class and noise are not used in an optimal manner. We apply a vector Wiener filter to photon-limited images degraded by atmospheric turbulence to demonstrate the potential advantages of optimal deconvolution processing. This filter incorporates model-based information about object, OTF, and noise. Computer simulation of binary star images show the vector Wiener filter provides superior reconstructions when compared to the traditional scalar Wiener filter for non- wide sense stationary objects. Much of this performance improvement can be attributed to superresolution and variance reduction in the noisy Fourier data at spatial frequencies where the mean OTF is severely attenuated. However, vector Wiener filter performance is substantially degraded with respect to both mean square error and mean square phase error at spatial frequencies where the OTF SNR is less than unity.
Postprocessing of images obtained from shear beam imaging
Brian A. Corser, Thomas F. Krile
In this paper it is shown that several image processing techniques can be employed to reduce the noise and improve the overall quality of images obtained from Shear-Beam- Imaging. Presented are several standard techniques used in the suppression of signal dependent noise, speckle in this case. While these techniques are shown to be adequate when speckle is the predominant noise source, they become less effective as the signal independent, or detector, noise increases. To this end we also propose a technique to effectively deal with both the signal dependent and signal independent noise in these images.
Examination of the optical transfer function from single-frame coherent speckle images
Barbara Tehan Landesman, David F. Olson
In classical imaging, the optical transfer function (OTF) conveys information about how well the optical system transmits individual spatial frequencies of the object. This OTF is based on the point spread function of the system; that is, the ability of the optics to form a point image given either coherent or incoherent illumination. In contrast, nonconventional imaging systems consist of an innovative combination of optics and software to form a final image. Such a system does not easily lend itself to the concept of a point spread function although individual spatial frequencies will be affected differently by the system as a whole. This paper investigates a phase differencing technique for deriving OTF information from a single frame of a coherent speckle image. A multiframe transfer function is obtained by averaging the OTFs of several single frames.
Determination of speckle size and object support from autocorrelation of speckle pattern arrays
David F. Olson, Robert E. Pierson
This paper describes the use of an auto-correlation technique to determine the minimum speckle size of a speckle pattern collected by a focal plane array of pixels. Object support for initialization of speckle image processing algorithms, as well as processing applicability, may be determined from radial speckle size information.
Polarization diversity active imaging
Polarization diversity active imaging is a new active imaging technique which illuminates a scene or target with a sequence of polarization states and then measures images of the polarization state scattered from a scene. These polarization images are then analyzed to determine the polarization characteristics at each pixel by measuring the Mueller matrix image, then mapping the retardance, diattenuation, and depolarization images over the scene. These data sets are used to estimate the plane of incidence and target orientation pixel by pixel.
Phase Retrieval
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3D reconstruction of opaque objects from Fourier intensity data
Michael F. Reiley, Richard G. Paxman, James R. Fienup, et al.
3D imaging provides important profile information not available with conventional 2D image products. Profile information can be extremely valuable for industrial- inspection and remote target-characterization applications. In this paper, we discuss a novel imaging modality, called PROCLAIM, that utilizes the powerful constraint that opaque objects can be described by a 2D surface embedded in 3D space. Far-field Fourier intensity measurements are collected by flood-illuminating an object with a frequency- tunable laser and direct detecting the backscattered signal with a lensless sensor. This technique allows for precise, non-contract surface measurements, without the stringent coherence and mechanical stability requirements of related interferometric techniques. We present reconstruction results form simulated data and from laboratory measurements.
3D locator sets of opaque objects for phase retrieval
James R. Fienup, Brian J. Thelen, Michael F. Reiley, et al.
Generating a 3D image can be accomplished by gathering 3D far-field heterodyne array data with multiple laser wavelengths and performing a 3D Fourier transform. However, since heterodyne detection is difficult at optical frequencies, the collection system can be greatly simplified if direct detection is performed instead. Then to reconstruct an image one would need a phase-retrieval algorithm. To assist the reconstruction algorithm, we place bounds on the support of the illuminated object, derived from the support of the autocorrelation function, which can be computed from the Fourier intensity data. We have developed 3D locator sets for getting tight bounds on the object support. These new locator sets are more powerful than those for 2D imaging, and some of them make explicit use of the fact that the illuminated opaque object is effectively a 2D surface embedded in 3D space. For those cases in which it is tight enough, the locator set itself may be all that we need to give an accurate height profile of the object.
Phase estimation from transmitted-light DIC images using rotational diversity
Chrysanthe Preza, Donald L. Snyder, Frederick U. Rosenberger, et al.
Differential-interference-contrast (DIC) microscopy is a powerful technique for the visualization of unstained transparent specimens, thereby allowing in vivo observations. Quantitative interpretation of DIC images is difficult because the measured intensity is nonlinearly related to the gradient of a specimen's optical-path-length distribution along the shear direction. The recent development of reconstruction methods for DIC microscopy permits the calculation of a specimen's optical-path-length distribution or phase function and provides a new measurement technique for biological applications. In this paper we present a summary of our work on quantitative imaging with a DIC microscope. The focus of our efforts has been in two areas: 1, model development and testing for 3D DIC imaging; and 2, development of a phase-estimation method based on this model. Our method estimates a specimen's phase function using rotational-diversity DIC images, i.e. multiple DIC images obtained by rotating the specimen. Test objects were viewed with a conventional DIC microscope using monochromatic light, and images were recorded using a cooled CCD camera. Comparison of the images to model predictions show good qualitative and quantitative agreement. Results obtained from testing the phase-estimation method with 2D simulations and with measured DIC images demonstrate that an estimate of an object's phase function can be obtained even from a single DIC image and that the estimated phase becomes quantitatively better as the number of rotational-diversity DIC images increases.
New technique for reconstruction of a complex wave field by means of measurement of three-dimensional intensity
Jinhong Tu, Shinichi Tamura
In this paper a new method for 2D complex wave reconstruction is developed by measurement of 3D intensity in a first order optical system under partially coherent illumination. The system includes two cylindrical lenses oriented along two perpendicular axes in a plane perpendicular to the propagation axis. When the parameters of the 2D lens system are set to satisfy the conditions of fractional Fourier transform independently in both dimensions, the input complex wave can be determined by measurements of intensities in a set of planes, and the mutual intensity is calculated through integrals of distributional coordinates and the fractional orders of fractional Fourier transform. As a result, the case of partially coherent illumination of Gaussian Schell-model is studied. In the numerical simulation it is found that phase structure in the input planes might be retrieved by this method in this system. The approach may provide an alternative way of recovering the phase object.
Phase retrieval from undersampled intensity data
Rick P. Millane, W. J. Stroud
An algorithm is described for incorporating symmetry information into reconstruction of an image from the amplitude of its Fourier transform. The symmetry is used to compensate for the loss of information due to sampling of the Fourier amplitude below the Nyquist density. The study is motivated by an image reconstruction problem in x-ray crystallography. Application of the algorithm to a simulated crystallographic problem shows that it converges to the correct solution, with no initial phase information, where algorithms currently used in crystallography fail. The results lend support to the possibility of ab initio phase retrieval in macromolecular crystallography when sufficient ta priori information is available.
Remote Sensing Applications
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Satellite image destriping: a wavelet-based approach
Jorge Torres, Jesus Favela
Scanning-radiometer imagery commonly displays systematic line stripes originated by differences in the sensibility of individual detectors. Traditionally, this noise has been eliminated by convolution techniques using digital filters. In this work we propose the sue of the wavelet transform as a technique for directional filtering. The method was tested in a Landsat multispectral scanner image having severe band striping. Since its basis functions are localized in the frequency and time domain, the wavelet transform performed a more selective analysis of the data, identifying the noise patterns in the image and allowing their remotion without data degradation.
Enhanced-resolution ERS-1 scatterometer imaging with irregular samples
David G. Long, David S. Early
Scatterometers are low resolution radars originally designed o measure winds over the ocean from space. They measure the normalized radar backscatter coefficient from which the wind is estimated. Over land and ice (sigma) 0 is very sensitive to surface conditions and is useful for various scientific studies. Unfortunately, the low resolution of the measurements limits the application of the data. The scatterometer image reconstruction (SIR) algorithm can produce significantly enhanced resolution radar images by taking advantage of measurement overlap from multiple passes of the radar over the target site. The resulting measurements are on an irregular grid and may have different response functions making the analysis of the non-linear SIR algorithm very complicated. Analysis of SIR is further complicated by the fact that it is bivariate: two separate but related images (A and B) are determined from the (sigma) 0 measurements where (sigma) 0 is related to A and B by the expression (sigma) 0 equals A + B ((theta) - 40 degrees) where (theta) is the incidence angle of the measurement which varies from measurement to measurement. In this paper we provide a theoretical framework for scatterometer image reconstruction and resolution enhancement on irregular grids and provide examples of the resolution enhancement possible for the ERS-1 AMI scatterometer. The paper should be of interest to other researchers dealing with resolution enhancement on irregular grids.
Intensity masking to get high-resolution images from low-quality apertures
The effort and expense required to build and maintain an optical-quality telescope increases dramatically with the size of the telescope aperture, and this is especially so in space. But scenarios have been proposed for deploying telescopes with very large but considerably less than optical-quality apertures. Our interest is in ameliorating the effects of the low quality aperture in order to exploit the raw size of the aperture to obtain high resolution images. We describe an algorithm for generating an adaptive binary mask to correct the time-varying aberrations of very large apertures which are many wavelengths out of figure. The technique is limited to monochromatic imagery, though the wavelength at which observations are taken can be easily changed on the fly, and for earth-pointing applications, the limited light-gathering power imposed by the monochromatic filter is not a problem. The mask itself can be placed at the exit pupil of the telescope, which permits implementation on a large scale. A similar approach, in which the pixels of the mask are half-wave phase shifters instead of opaque optical elements, was described by Love et al.
Restoration of fragments of overcast video images with the use of a priori information
Vladimir V. Belov, Konstantin T. Protasov
In the solution of problems of ecological monitoring of the Earth's underlying surface, the multichannel satellite information is the main type of data obtained in real time that can be used to estimate the most important parameters of natural complexes. It is well known that interpretation of videoimages recorded under conditions of broken clouds involves problems when some regions of the Earth's surface are overcast by dense fog or cloud cells of high optical density. In this case, application of standard methods for image restoration based, for example, on the linear model describing the image transfer through dense scattering media in the form of the convolution functional of the sought-after image with the point spread function gives no way of obtaining results of any value. In this connection, we consider statistical methods for a solution of this problem.
Image Deblurring and Superresolution
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Grouped coordinate descent algorithms for robust edge-preserving image restoration
We present a new class of algorithms for edge-preserving restoration of piecewise-smooth images measured in non- Gaussian noise under shift-variant blur. The algorithms are based on minimizing a regularized objective function, and are guaranteed to monotonically decrease the objective function. The algorithms are derived by using a combination of two previously unconnected concepts: A. De Pierro's convexity technique for optimization transfer, and P. Huber's iteration for M-estimation. Convergence to the unique global minimum is guaranteed for strictly convex objective functions. The convergence rate is very fast relative to conventional gradient-based iterations. The proposed algorithms are flexibly parallelizable, and easily accommodate non-negativity constraints and arbitrary neighborhood structures. Implementation in Matlab is remarkably simple, requiring no cumbersome line searches or tolerance parameters.
Superresolution algorithms for SAR images
Veronique Guglielmi, Francis Castanie, P. Piau
We present five algorithms which can improve classical resolution of synthetic aperture radar images, especially when the objects of interest are small bright target are small bright targets against a weaker background. Through quantitative analysis of the resolution enhancement, we assess their different performances.
Image restoration in multisensor missile seeker environments for design of intelligent integrated processing architectures
Malur K. Sundareshan, Ho-Yuen Pang, Sengvieng A. Amphay, et al.
Two major factors that could limit successful implementations of image restoration and superresolution algorithms in missile seeker applications are, (i) lack of accurate knowledge of sensor point spread function (PSF) parameters, and (ii) noise-induced artifacts in the restoration process. The robustness properties of a recently developed blind iterative Maximum Likelihood (ML) restoration algorithm to inaccuracies in sensor PSF are established in this paper. Two modifications to this algorithm that successfully equip it to suppress artifacts resulting from the presence of high frequency noise components are outlined. Performance evaluation studies with 1D and 2D signals are included to demonstrate that these algorithms have superresolution capabilities while possessing also attractive robustness and artifact suppression properties. The algorithms developed here hence contribute to efficient designs of intelligent integrated processing architectures for smart weapon applications.
Reconstruction of step edges with subpixel accuracy in gray-level images
Jose M. Sebastian y Zuniga, Oscar Reinoso, Rafael Aracil, et al.
Many inspection methods using computer vision have been developed, although in many of them the results obtained do not have the desired accuracy. In order to increase the system precision, two different solutions can be considered: the use of a more powerful image acquisition equipment and a solution that consists in developing algorithms that allow us to increase the accuracy of certain characteristics of the image. This paper is focused on setting a model that takes into account all the different signals involved in the image processing. It also defines the basis for the reconstruction of images in those areas with high content of information, such as edges, and more specifically those edges with a high change of intensity. In the image acquisition process, the input information is perfectly defined in a continuous domain and a discrete image is obtained as output, although distorted by the effects of the lenses, electrical sensor and the digitizer. This paper defines the conditions that the sampling process must satisfy in order to make possible the reconstruction of step edges using non-linear reconstruction filters in gray level images.
Bayesian image reconstruction from partial image and spectral amplitude data
Shyamsunder Baskaran, Rick P. Millane
We address a problem of reconstruction of a periodic image from information in image space and Fourier space. The real space information consists of knowledge of part of the image, while the Fourier space information is data in the form of sums of the squares of the amplitudes of sets of particular Fourier coefficients of the image. Such a problem occurs in the determination of polymer structures from x-ray fiber diffraction data. We present a Bayesian approach to this problem, incorporating a priori model for the image based on the structure being made up of 'atoms'. The Bayesian minimum mean-square-error estimate for the missing part of the image is derived. Currently used heuristic estimates are the maxima of certain posterior densities. Simulations are performed for varying amounts of real and Fourier space information to assess the performance of the different estimators. The performance of the minimum mean- square-error estimate is superior to that of the other estimates.
Computed Tomography
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Shape reconstruction in x-ray tomography
X-ray tomographic image reconstruction consists in determining an object function from its projections. In many applications such as non-destructive testing, we look for a default region in a homogeneous known background. The image reconstruction problem becomes then the determination of the shape of the default region. Two approaches can be used: modeling the image as a binary Markov random field and estimating the whole pixels of the image or modeling the shape of the default and estimating it directly from the projections. In this work we model the default shape by a polygonal disc and propose a new method for estimating directly the coordinates of its vertices from a very limited number of its projections. The idea is not new, but in other competing methods, in general, the default shape is modeled by a small number of parameters and these parameters are estimated either by least squares or by maximum likelihood methods. What we propose is to model the shape of the default region by a polygon with a great number of vertices to be able to model any shapes and to estimate directly its vertices coordinates from the projections by defining the solution as the minimizer of an appropriate regularized criterion which can also be interpreted as a maximum a posteriori estimate in a Bayesian estimation framework. To optimize this criterion we use either a simulated annealing or a special purpose deterministic algorithm based on iterated conditional modes. The simulated results are very encouraging specially when the number and the angels of projections are very limited. Some comparisons with classical methods are provided to show the performances of the proposed method.
Quantitative effects of using thin-plate priors in Bayesian SPECT reconstruction
Maximum a posteriori approaches in the context of a Bayesian framework have played an important role in SPECT reconstruction. The major advantages of these approaches include not only the capability of modeling the character of the data in a natural way but also the allowance of the incorporation of a priori information. Here, we show that a simple modification of the conventional smoothing prior, such as the membrane prior, to one less sensitive to variations in first spatial derivatives - the thin plate (TP) prior - yields improved reconstructions in the sensor of low bias at little change in variance. Although the nonquadratic priors, such as the weak membrane and the weak plate, can exhibit good performance, they suffer difficulties in optimization and hyperparameter estimation. On the other hand, the thin plate, which is a quadratic prior, leads to easier optimization and hyperparameter estimation. In this work, we evaluate and compare quantitative performance of MM, TP, and FBP algorithms in an ensemble sense to validate advantages of the thin plate model. We also observe and characterize the behavior of the associated hyperparameters of the prior distributions in a systematic way. To incorporate our new prior in a MAP approach, we model the prior as a Gibbs distribution and embed the optimization within a generalized expectation- maximization algorithm. For optimization for the corresponding M-step objective function, we use a version of iterated conditional mode. We show that the use of second- derivatives yields 'robustness' in both bias and variance by demonstrating that TP leads to very low bias error over a large range of smoothing parameter, while keeping a reasonable variance.
Adaptive helical computed tomography reconstruction for MIP artifact reduction
Helical computed tomography has become the preferred patient scanning mode in many clinical applications. A number of comparative studies have been performed to evaluate its performance parameters, such as the noise and the slice sensitivity profile. The objective of this paper is to examine the non-stationary noise characteristics of helical images and demonstrate its impact on the 3D image artifacts. We first derive an analytical equation that relate the interactions between the helical reconstruction scheme and the fan-beam filtered backprojection algorithm. We demonstrate that for many popular helical weights, the nose variation within the field of view of the reconstruction is close to a factor of 3. An adaptive approach to the reduction of the artifacts is proposed.
Remote Sensing Applications
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Cramer-Rao analysis of phase diversity imaging
David J. Lee, Byron M. Welsh, Michael C. Roggemann
Phase diversity wavefront sensing (PDWFS) is concerned with estimating aberration coefficients from multiple images collected with known differences in pupil phase. Using previous work by other authors, the Cramer-Rao lower-bound (CRLB) expression for the phase diversity aberration estimation problem is developed, generalized slightly to allow for multiple diversity images, various beamsplitting configurations, and the imaging of extended objects. The CRLB for a given problem depends on the actual value of the aberration being stated. Therefore, we turn to numerical simulation and a Monte Carlo analysis of the CRLBs of an ensemble of simulated aberration phase screens and draw tentative conclusions about various phase diversity imaging situations. The 'average' CRLB value for a given phase screen ensemble and imaging scenario is used as a figures of merit in comparing various PDWFS configurations. For simulated point-source imaging, we quantify the impact of varying the amounts of focus diversity, both symmetrically to both images, and asymmetrically, to a single image. We find reason to believe that a symmetrically defocused image collection scheme may be more advantageous for PDWFS. We also explore the impact of splitting the light among two images asymmetrically, as well as splitting the light among three images. Deviations from a traditional 50-50 beamsplit among 2 images are shown to be disadvantageous in a CRLB sense.Finally we verify that CRLB values are orders of magnitude higher for imaging of an extended object, when compared to point-source PDWFS imaging.