The basis of phase dominance.

Phase dominance is a phenomenon that has been widely observed in imaging, visual perception, and other technical areas. Here we show for general images that phase dominance, in terms of exchanging the spectral amplitude and phase of two images, is simply explained by the expected mean square error.

Two-point correlation function for the triangular Ising antiferromagnet.

A number of aspects of the two-point correlation behavior of the nearest-neighbor, triangular Ising antiferromagnet are studied using a combination of numerical evaluation of exact expressions and Monte Carlo simulation. Existing asymptotic results for on-axis correlations at finite temperatures are evaluated and shown to be of limited accuracy. The sublattice structure of the off-axis correlation function is clarified, and rotational invariance is studied as a function of temperature. Separations and temperatures for which the correlation function is significant are identified, and a simple functional expression is developed that allows accurate calculation of the correlation function in this region.

Determination of molecular envelopes from solvent contrast variation data.

An algorithm is described for determining macromolecular envelopes from crystal diffraction amplitudes measured from a solvent contrast variation series. The method uses solvent contrast variation data that have been preprocessed to represent the structure-factor amplitudes of the envelope. The amplitudes are phased using an iterative projection algorithm that incorporates connectivity and compactness constraints on the envelope. The algorithm is tested by simulation on two protein envelopes and shown to be effective even in the absence of the very low resolution data, which are difficult to access experimentally.

Determination of myosin filament orientations in electron micrographs of muscle cross sections.

An automated image analysis system for determining myosin filament azimuthal rotations, or orientations, in electron micrographs of muscle cross sections is described. The micrographs of thin sections intersect the myosin filaments which lie on a triangular lattice. The myosin filament profiles are variable and noisy, and the images exhibit a variable contrast and background. Filament positions are determined by filtering with a point spread function that incorporates the local symmetry of the lattice. Filament orientations are determined by correlation with a template that incorporates the salient filament characteristics, and the orientations are classified using a Gaussian mixture model. The precision of the technique is assessed by application to a variety of micrographs and comparison with manual classification of the orientations. The system provides a convenient, robust, and rapid means of analysing micrographs containing many filaments to study the distribution of filament orientations.

Improved matrix inversion in image plane parallel MRI.

A new 3D parallel magnetic resonance imaging (MRI) method named Generalized Unaliasing Incorporating Support constraint and sensitivity Encoding (GUISE) is presented. GUISE allows direct image recovery from arbitrary Cartesian k-space trajectories. However, periodic k-space sampling patterns are considered for reconstruction efficiency. Image recovery methods such as 2D SENSE (SENSitivity Encoding) and 2D CAIPIRINHA (Controlled Aliasing In Parallel Imaging Results IN Higher Acceleration) are special instances of GUISE where specific restrictions are placed on the k-space sampling patterns used. It is shown that the sampling pattern has large impacts on the image reconstruction error due to noise. An efficient sampling pattern design method that incorporates prior knowledge of object support and coil sensitivity profile is proposed. It requires no experimental trials and could be used in clinical imaging. Comparison of the proposed sampling pattern design method with 2D SENSE and 2D CAIPIRINHA are made based on both simulation and experiment results. It is seen that this new adaptive sampling pattern design method results in a lower noise level in reconstructions due to better exploitation of the coil sensitivity variation and object support constraint. In addition, elimination of the non-object region from reconstruction potentially allows an acceleration factor higher than the number of receiver coils used.

Reconstruction of compact binary images from limited Fourier amplitude data.

The problem of reconstructing a binary image from undersampled Fourier amplitude data is considered. This problem maps to an image reconstruction problem in x-ray crystallography. The binary constraint is sufficient to overcome the undersampling and enforce uniqueness, but is insufficient in the case of the additional loss of data that can occur in practice. An iterative projection algorithm is developed that uses binary, connectivity, and compactness constraints to solve the image reconstruction problem. Simulations show the utility of the reconstruction algorithm.

Automated analysis of differential interference contrast microscopy images of the foveal cone mosaic.

An algorithm is presented for processing and analysis of differential interference contrast (DIC) microscopy images of the fovea to study the cone mosaic. The algorithm automatically locates the cones and their boundaries in such images and is assessed by comparison with results from manual analysis. Additional algorithms are presented that analyze the cone positions to extract information on cone neighbor relationships as well as the short-range order and domain structure of the mosaic. The methods are applied to DIC images of the human fovea.

Reconstruction of an object from its symmetry-averaged diffraction pattern.

The problem of reconstructing an object from diffraction data that has been incoherently averaged over a discrete group of symmetries is considered. A necessary condition for such data to uniquely specify the object is derived in terms of the object support and the symmetry group. An algorithm is introduced for reconstructing objects from symmetry-averaged data and its use with simulations is demonstrated. The results demonstrate the feasibility of structure determination using a recent proposal for aligning molecules by means of their anisotropic dielectric interaction with an intense light field

MRI with TRELLIS: a novel approach to motion correction.

A motion-correcting pulse sequence and reconstruction algorithm, termed TRELLIS, is presented. k-Space is filled using orthogonal overlapping strips and the directions for phase- and frequency-encoding are alternated such that the frequency-encode direction always runs lengthwise along each strip. The overlap between strips is used both for signal averaging and to produce a system of equations that, when solved, quantifies the rotational and translational motion of the object. Results obtained from simulations with computer-generated phantoms, a purpose-built moving phantom, and in human subjects show the method is effective. TRELLIS offers some advantages over existing techniques in that k-space is sampled uniformly and all acquired data are used for both motion detection and image reconstruction.

A modified view ordering for artifact reduction in MRI.

Fast spin echo (FSE) is a means of rapidly acquiring k-space data in magnetic resonance imaging (MRI). Unfortunately, images obtained using FSE often contain artifacts. These are caused primarily by patient motion and transversal magnetisation decay, the latter being characterised by the time constant T2. This paper presents a study of the effect of data acquisition order on the severity of these effects.

Effects of Fourier-plane amplitude and phase errors on image reconstruction. I. Small amplitude errors.

The effects of Fourier-plane, or spectral, amplitude and phase errors on reconstructed images are studied in terms of the expected mean square error in the image. The relationship between the variance of amplitude and phase errors and the expected mean square error is derived for small amplitude errors and arbitrarily large phase errors. This allows "equivalent" amplitude and phase errors to be defined. The effects of large amplitude errors are discussed in general terms. Simulations are used to verify these relationships, and the effects of spectral amplitude and phase errors on reconstructed images are compared.

Image spectral amplitude distributions.

Models for the probability density functions of the Fourier amplitude of images are derived. The densities are based on a simple model of an image made up of independent objects and incorporates the observed behavior of the circularly averaged power spectrum versus spatial frequency. The density function over all spatial frequencies gives a good fit to spectral amplitude data from a variety of images.

Triangular Ising antiferromagnet: boundary conditions, ground state entropy, and vortices.

The ground state entropy density of the triangular Ising antiferromagnet is considered as a function of boundary conditions on domains for which the ground states do not admit a dimer covering. These domains admit a rich set of ground states that cannot be classified in the usual way in terms of nonintersecting strings. Various parametrized boundary conditions and domain shapes are identified that allow the ground state entropy density to be varied between zero and maximal degeneracy. The dependence of degeneracy on boundary spins and/or domain shape is interpreted in terms of strings that are not restricted to be nonintersecting.

Effects of occlusion, edges, and scaling on the power spectra of natural images.

The circularly averaged power spectra of natural image ensembles tend to have a power-law dependence on spatial frequency with an exponent of approximately -2. This phenomenon has been attributed to object occlusion, the presence of edges, and scaling of object sizes (self-similarity) in natural scenes, although the relative importance of these properties is still unclear. A detailed examination of the effects of occlusion, edges, and self-similarity on the behavior of the power spectrum is conducted using a simple model of natural images. Numerical simulations show that edges and self-similarity are necessary for a power-law power spectrum over a wide range of spatial frequencies. Object occlusion is not an essential factor. A theoretical analysis for images containing nonoccluding objects supports these results.

Boundary conditions and variable ground state entropy for the antiferromagnetic Ising model on a triangular lattice.

The ground state entropy density of the antiferromagnetic Ising model on a triangular lattice is considered in the infinite volume limit as a function of boundary conditions on a finite triangular domain. The ground states of this domain do not map to a dimer covering and so cannot be classified into string sectors. A parametrized boundary condition is identified that allows the entropy density to be tuned to values between nondegeneracy and maximal degeneracy. The results are compared to those for a rectangular periodic domain for which the ground states can be classified into string sectors.

Fluorescence optical diffusion tomography using multiple-frequency data.

A method is presented for fluorescence optical diffusion tomography in turbid media using multiple-frequency data. The method uses a frequency-domain diffusion equation model to reconstruct the fluorescent yield and lifetime by means of a Bayesian framework and an efficient, nonlinear optimizer. The method is demonstrated by using simulations and laboratory experiments to show that reconstruction quality can be improved in certain problems through the use of more than one frequency. A broadly applicable mutual information performance metric is also presented and used to investigate the advantages of using multiple modulation frequencies compared with using only one.

Fluorescence optical diffusion tomography.

A nonlinear, Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the diffusion coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and the emission wavelengths to reconstruct all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental data from a tissue phantom containing the fluorescent agent Indocyanine Green.

On apparent counterexamples to phase dominance.

Phase dominance refers to the observation that the phase of the Fourier transform of an image carries more information than does the amplitude. We show that apparent counterexamples to phase dominance are not in fact counterexamples since the phase functions used are not independent of the true phase function. Phase dominance appears to be a general phenomenon.

Efficient frequency-domain sample selection for recovering limited-support images.

An image whose region of support is smaller than its bounding rectangle can, in principle, be reconstructed from a subset of the Nyquist samples. However, determining such a sampling set that gives a stable reconstruction is a difficult and computationally intensive problem. An algorithm is developed for determining periodic nonuniform sampling patterns that is orders of magnitude faster than existing algorithms. The speedup is achieved by using a sequential selection algorithm and heuristic metrics for the quality of sampling sets that are fast to compute, as opposed to the more rigorous linear algebraic metrics that have been used previously. Simulations show that the sampling sets determined using the new algorithm give image reconstructions that are of accuracy comparable with those determined by other slower algorithms.

Source-detector calibration in three-dimensional Bayesian optical diffusion tomography.

Optical diffusion tomography is a method for reconstructing three-dimensional optical properties from light that passes through a highly scattering medium. Computing reconstructions from such data requires the solution of a nonlinear inverse problem. The situation is further complicated by the fact that while reconstruction algorithms typically assume exact knowledge of the optical source and detector coupling coefficients, these coupling coefficients are generally not available in practical measurement systems. A new method for estimating these unknown coupling coefficients in the three-dimensional reconstruction process is described. The joint problem of coefficient estimation and three-dimensional reconstruction is formulated in a Bayesian framework, and the resulting estimates are computed by using a variation of iterative coordinate descent optimization that is adapted for this problem. Simulations show that this approach is an accurate and efficient method for simultaneous reconstruction of absorption and diffusion coefficients as well as the coupling coefficients. A simple experimental result validates the approach.