This PDF file contains the Front Matter associated with SPIE Proceedings volume 7800, including the Title page, Copyright information, Table of Contents, Conference Committee listing, and Introduction.

Advanced manifold-based techniques can be used to determine the structure and dynamics of an evolving object from a collection of ultra-low-signal, two-dimensional snapshots emanating from unknown orientations and conformations.

Photoacoustic tomography is a rapidly emerging imaging technique that can benefit a wide range of biomedical applications. In this method, illumination of an object with a pulsed optical field induces an acoustic pressure wave related to the heating of the object (optical absorption). From knowledge of the resultant pressure wave measured in a region away from the acoustic source, the object's spatially varying optical absorption properties are estimated by use of an image reconstruction algorithm. Most existing analytic reconstruction algorithms for photoacoustic tomography assume the object of interest possesses homogeneous acoustic properties. In this work, photoacoustic tomography is considered in the case that the primary acoustic source is embedded in a planar layered medium whose speed of sound and densities are known. Exact propagation models valid for acoustic wave propagation in dispersive and absorptive layered media are presented that account for multiple reflections between the layers. Using the angular spectrum method, an inversion model is presented for acoustic data acquired on a plane parallel to the layered medium. The acquired data are shown to be simple linear combinations of plane waves generated at the source.

Optoacoustic tomography (OAT) is an emerging ultrasound-mediated biophotonic imaging modality that has exciting potential for many biomedical imaging applications. There is great interest in conducting B-mode ultrasound and OAT imaging studies for breast cancer detection using a common transducer. In this situation, the range of tomographic view angles is limited, which can result in distortions in the reconstructed OAT image if conventional reconstruction algorithms are applied to limited-view measurement data. In this work, we investigate an image reconstruction method that utilizes information regarding target boundaries to improve the quality of the reconstructed OAT images. This is accomplished by developing boundary-constrained image reconstruction algorithm for OAT based on Bayesian image reconstruction theory. The computer-simulation studies demonstrate that the Bayesian approach can effectively reduce the artifact and noise levels and preserve the edges in reconstructed limited-view OAT images as compared to those produced by a conventional OAT reconstruction algorithm.

Cepstral filtering is reviewed as a suitable and efficient method to solve the inverse scattering problem in the case of strongly scattering permittivity distributions. The number and distribution of measured scattered field data required is discussed, as is the effective number of degrees of freedom available to describe the scattering structure. The latter is identified as a key parameter determining the performance of the cepstral method. This is of particular importance for strong scattering and nonlinear image processing methods since many data sets are compiled based on the sampling requirements of weakly scattering objects. We find that the domain of the object support and the maximum permittivity contrast are important prior information for determining the minimum number of data samples necessary while maximizing use of the available degrees of freedom; examples are presented.

In MRI, non-rectilinear sampling trajectories are applied in k-space to enable faster imaging. Traditional image reconstruction methods such as a fast Fourier transform (FFT) can not process datasets sampled in non-rectilinear forms (e.g., radial, spiral, random, etc.) and more advanced algorithms are required. The Fourier reduction of optical interferometer data (FROID) algorithm is a novel image reconstruction method^1-3 proven to be successful in reconstructing spectra from sparsely and unevenly sampled astronomical interferometer data. The framework presented allows a priori information, such as the locations of the sampled points, to be incorporated into the reconstruction of images. In this paper, the FROID algorithm has been adapted and implemented to reconstruct magnetic resonance (MR) images from data acquired in k-space where the sampling positions are known. Also, simulated data, including randomly sampled data, are tested and analyzed.

A method to improve time resolution in 3D contrast-enhanced magnetic resonance angiography (CE-MRA) is proposed. A temporal basis based on prior knowledge of the contrast flow dynamics is applied to a sequence of image reconstructions. In CE-MRA a contrast agent (gadolinium) is injected into a peripheral vein and MR data is acquired as the agent arrives in the arteries and then the veins of the region of clinical interest. The acquisition extends over several minutes. Information is effectively measured in 3D k-space (spatial frequency space) one line at-atime. That line may be along a Cartesian grid line in k-space, a radial line or a spiral trajectory. A complete acquisition comprises many such lines but in order to improve temporal resolution, reconstructions are made from only partial sets of k-space data. By imposing a basis for the temporal changes, based on prior expectation of the smoothness of the changes in contrast concentration with time, it is demonstrated that a significant reduction in artifacts caused by the under-sampling of k-space can be achieved. The basis is formed from a set of gamma variate functions. Results are presented for a simulated set of 2D spiral-sampled CE-MRA data.

X-ray phase-contrast tomography (PCT) methods seek to quantitatively reconstruct separate images that depict an object's absorption and refractive properties. Most PCT reconstruction algorithms generally operate by explicitly or implicitly performing the decoupling of the projected absorption and phase properties at each tomographic view angle by use of a phase-retrieval formula, followed by the inversion of X-ray transform. Tomographic reconstruction by use of statistical methods can account for the noise model and a priori information, and thereby can produce images with better quality over conventional filtered backprojection algorithms. We proposed a weighted least-squares method that takes into account the second-order statistical properties of the projected phase images and aims to minimize the objective function by employing a conjugate-gradient (CG) method. A computer-simulation study was carried out to investigate and evaluate the developed method.

The author presents the maximum a posteriori (MAP) estimation method to estimate irradiance elemental images and reconstruct 3D images using photon-counting integral imaging. Elemental images are captured using the synthetic aperture integral imaging (SAII) technique. Photon-counting elemental images are generated using the Poisson distribution. The method can reconstruct 3D images more accurately than the one using maximum likelihood (MLE) estimation. This may be important in medical imaging as well as other photon-level applications.

The problem of estimating the wind velocity from measurement of limited flight data from a sailplane flight in atmospheric mountain waves is considered. A Sailplane are often equipped with a flight recorder that records position, and sometimes other information, at regular intervals during the flight. These data contain information on the state of the atmosphere during the flight. A maximum likelihood method is developed for estimating wind fields using such sailplane flight data. The methods are evaluated by application to simulated flight data.

The solar-reflected brightness distribution of a man-made space object has regions of spatially uniform brightness and spectral content that are interrupted only by boundaries separating one material region from another. The relatively simple structure of this distribution permits, as we demonstrate here, spectral-correlation-based strategies to extract information about the boundaries and material constituents of the segments of the object surface. Still simpler compressive-sensing (CS) based approaches that require no specific spectral analysis can also efficiently perform such information extraction, which is a critical task of any space-object identification (SOI) system. We analyze here these latter approaches by means of statistical information theory (IT) in the context of a highly idealized satellite model with rectilinear material boundaries and quasi-one-dimensional (1D) brightness distribution. Our analysis includes spectrally dependent diffractive blur as well as detector noise against which we optimize, via our IT calculations, the choice of the CS mask set, the bandwidth of the spectral measurements, and the minimum number of measurements needed for extracting information about the boundary locations and material identities.

In this paper, we describe a practical implementation of an image reconstruction method designed to generate a map of the brightness distribution from data consisting of squared visibilities and complex closure amplitudes resulting from observations of an astronomical target with a broadband, multichannel, spatial optical interferometer. Given the data, the method estimates the true brightness distribution with a model sampled on a rectangular grid of discrete positions on the sky with the assumption that the model intensities in the region not defined by the discrete positions being described by bilinear interpolation of the discrete intensities. The developed image reconstruction method has been applied to real observational data obtained from existing optical interferometer facilities.

When x-rays penetrate soft matter, their phase changes more rapidly than their amplitude. Interference effects visible with high brightness sources creates higher contrast, edge enhanced images. When the object is piecewise smooth (made of big blocks of a few components), such higher contrast datasets have a sparse solution. We apply basis pursuit solvers to improve SNR, remove ring artifacts, reduce the number of views and radiation dose from phase contrast datasets collected at the Hard X-Ray Micro Tomography Beamline at the Advanced Light Source. We report a GPU code for the most computationally intensive task, the gridding and inverse gridding algorithm (non uniform sampled Fourier transform).

Image registration is one of the most important tasks in image processing and is frequently one of the most computationally intensive. In cases where there is a high likelihood of finding the exact template in the search image, correlation-based methods predominate. Presumably this is because the computational complexity of a correlation operation can be reduced substantially by transforming the task into the frequency domain. Alternative methods such as minimum Sum of Squared Differences (minSSD) are not so tractable and are normally disfavored. This bias is justified when dealing with conventional computer processors since the operations must be conducted in an essentially sequential manner however we demonstrate it is normally unjustified when the processing is undertaken on customizable hardware such as FPGAs where tasks can be temporally and/or spatially parallelized. This is because the gate-based logic of an FPGA is better suited to the tasks of minSSD i.e. signed-addition hardware can be very cheaply implemented in FPGA fabric, and square operations are easily implemented via a look-up table. In contrast, correlationbased methods require extensive use of multiplier hardware which cannot be so cheaply implemented in the device. Even with modern DSP-oriented FPGAs which contain many "hard" multipliers we experience at least an order of magnitude increase in the number of minSSD hardware modules we can implement compared to cross-correlation modules. We demonstrate successful use and comparison of techniques within an FPGA for registration and correction of turbulence degraded images.

When imaging through the atmosphere, the resulting image contains not only the desired scene, but also the adverse effects of all the turbulent air mass between the camera and the scene. These effects are viewed as a combination of nonuniform blurring and random shifting of each point in the received short-exposure image. Corrections for both aspects of this combined distortion have been tackled reasonably successfully by previous efforts. We presented in an earlier paper a more robust method of restoring the geometry by redefining the place of the prototype frame and by reducing the adverse effect of averaging in the processing sequence. We present here a variant of this method using a Minimum Sum of Squared Differences (MSSD) cross-correlation registration algorithm implemented on a Graphics Processing Unit (GPU). The raw speed-up achieved using GPU code is in the order of x1000. Two orders of magnitude speed-up on the complete algorithm will allow for better fine tuning of this method and for experimentation with various registration algorithms.

The resolving power in optical imaging is limited not only by optical diffraction but also by the sampling size, which in turn is determined by the optical magnification and pixel size of the imaging devices such as CCD or CMOS. In order to exceed these limits, we propose a method for improving the optical resolving power by using structured illumination shift and multiple image reconstruction. Theoretical and experimental verifications reveal that the use of structured light illumination together with successive approximation (which provides the extrapolation effect) causes the resolving power of the proposed method to exceed the optical diffraction limit. Furthermore, we focused on subpixel sampling using the structured illumination shift method. Subpixel image processing can improve the resolving power without narrowing the visual field of the imaging optics. In addition, the proposed method can provide subpixel resolving power without necessitating the mechanical displacement of the CCD camera. We investigated the relationship between the CCD pixel size and the resolving power provided by the proposed method. We found that the subpixel spatial shift of the structured illumination not only improves the optical resolving power but also enables sub-pixel sampling for optical imaging.

Resolution of any image taken by CCD camera is generally lower in resolution in comparison with original object. Assuming the imaging system as diffraction limited - the major component responsible for this resolution limitation is the pixel geometry in CCD. The area, shape of pixel and distance between them (inter-pixel spacing) together contributes in reduction of the resolution of the final electronic image. A number of techniques have been reported in the literature to overcome this geometric resolution limitation. We have proposed a novel geometric superresolution technique in which a CCD-mask is displaced over CCD-plane by one pixel in subpixel steps - both in x and y directions. The resultant processed superresolved image is improved in resolution by the subpixel steps factor. Simulation results in 2D have been presented which shows improvement in resolution. This superresolution technique can be applied to microscopy, medical imaging, satellite imaging and astronomy.

In optical systems with quite good correction, the field-dependence of aberrations often can be neglected. In low performance systems, for the application of deconvolution methods the field-dependence of the point spread function must be taken into account. However, the number of publications dealing with the topic of space-variant deconvolution in order to compensate system aberrations is quite low. In this contribution, we investigate the fundamental difficulty accompanied by space-variant deconvolution, which makes the problem ill-posed, even in the case of non-vanishing modular transfer functions and the assumption of noise-free imaging. The spatial frequencies of the image spectrum are mixed depending on the field-dependencies of the optical aberrations. In general, it is therefore not possible to reconstruct the individual frequencies exactly. Some discrete examples with a non unique solution are presented. For the 2D case, we will show and investigate how the most popular algorithms deal with this fundamental problem for different typical types of optical aberrations. Depending on the aberration, the computational results for those algorithms differ from very good results to images with artifacts. The Lucy Richardson method, which is often recommended in the case of spaceinvariant image reconstruction since it may even reconstruct frequencies above the cut off frequency, provides poor results for unsymmetrical space-variant aberrations like Coma or a simple Tilt. However, we will show that a simpler method like the Landweber algorithm is better suited to deal with those kinds of aberrations.

A statistical estimation problem for determining 3-D reconstructions from a single 2-D projection image of each of multiple objects when the objects are heterogeneous is described. The method is based on a Gaussian mixture description of the heterogeneity and is motivated by cryo electron microscopy of biological objects.

The scattered radio image of a pulsar, as a result of the radio wave passing through the turbulent interstellar plasma, is a valuable probe of the plasma turbulence. However the scattering angles are so small, typically a few milli-arcsec, that the radio image cannot be resolved even with very long baseline interferometry (VLBI). Recently we ^[1] combined the secondary spectrum^[2] technique with VLBI astrometry to resolve the ambiguities in reconstructing the scattered image of pulsar B0834+06 at 327 MHz with an angular resolution 100 times finer than would have been possible with VLBI alone. However this technique can only reconstruct the outer portion of the image and it does not provide an estimate of the axial ratio of the plasma turbulence. Here we present a significant advancement of the technique which allows reconstruction of the central part of the image in two dimensions, providing an estimate of the axial ratio of the anisotropic turbulence. This technique relies on modeling a peculiar feature of the two dimensional Fourier transform of the dynamic spectrum (the secondary spectrum), called a "reverse arclet". For the 327 MHz observations of B0834+06 the secondary spectrum exhibits many identical reverse arclets. They originate from the interference between offset bright points and the core of the brightness distribution. The technique has also been tested using simulated data that confirms the image reconstruction algorithm.

Symmetry provides a source of redundancy which can be exploited in image reconstruction. In particular, internal symmetries in molecules can help to compensate for the loss of Fourier phase information in macromolecular x-ray crystallography. Symmetry projections are incorporated into iterative projection algorithms for reconstruction of macromolecular electron densities from x-ray diffraction amplitudes from crystals. The effects of interpolation are studied and the algorithms are applied to reconstruction of an icosahedral virus.

Diffraction from the individual molecules of a molecular beam, aligned parallel to a single axis by a strong electric field or other means, has been proposed as a means of structure determination of individual molecules. As in fiber diffraction, all the information extractable is contained in a diffraction pattern from incidence of the diffracting beam normal to the molecular alignment axis. We present two methods of structure solution for this case. One is based on the iterative projection algorithms for phase retrieval applied to the coefficients of the cylindrical harmonic expansion of the molecular electron density. Another is the holographic approach utilizing presence of the strongly scattering reference atom for a specific molecule.

The latest development of ultrafast free electron laser makes it now possible to perform single molecule diffraction imaging. In such an experiment, two-dimensional (2D) diffraction images of randomly oriented molecules of the same type (single molecules) can be captured within femtosecond exposure time. These images can then be used to deduce the 3D structure of the molecule. Two of the most challenging problems that must be solved in order to obtain a high resolution 3D reconstruction are: 1) the determination of the relative orientations of 2D diffraction images; 2) the retrieval of the phase information of a reconstructed 3D diffraction pattern. In this paper, we will focus on the first problem and discuss the use of common curve detection techniques to deduce the relative orientations of 2D diffraction images produced from single-molecule diffraction experiments. Such a technique is based on the fact that Ewald spheres associated with two diffraction images of the same molecule intersect along a common curve in the reciprocal space. By detecting these curves on each diffraction image, we can deduce the relative orientations of diffraction images by solving an eigenvalue problem. When the radius of the Ewald sphere is sufficiently large relatively to the region of reciprocal space we are interested in, the Ewald sphere becomes flat near the origin of the reciprocal space, and common curves reduce to common lines. In this case, the orientation determination problem is similar to the one that arises in single particle cryo-electron microscopy. The recent work of Singer and Shkolnisky [1] shows that the orientation determination problem can be solved by computing the largest eigenvalues of a symmetric matrix constructed from the common lines identified among cryo-EM projection images. In this paper, we will extend their technique to diffraction images on which common curves can be identified.

Cryo electron microscopy imaging experiments can lead to stochastic models for biological macromolecular complexes. However, interpreting the statistical variability is difficult. In some situations, the variability in the original complexes is due to primarily thermal fluctuations which are snap frozen in place by the preparation of the specimen. In this case the images are images of samples of the equilibrium statistical mechanics ensemble of the complex. Based on representing the complex by a lattice spring-mass mechanical model, an estimation problem for determining the masses and spring constants is described and demonstrated on synthetic data.

Cryo electron microscopy is frequently used on biological specimens that show a mixture of different types of object. Because the electron beam rapidly destroys the specimen, the beam current is minimized which leads to noisy images (SNR substantially less than 1) and only one projection image per object (with an unknown projection direction) is collected. For situations where the objects can reasonably be described as coming from a finite set of classes, an approach based on joint maximum likelihood estimation of the reconstruction of each class and then use of the reconstructions to label the class of each image is described and demonstrated on two challenging problems: an assembly mutant of Cowpea Chlorotic Mottle Virus and portals of the bacteriophage P22.