Mask design, fabrication, and experimental ghost imaging applications for patterned X-ray illumination.

A set of non-configurable transversely-displaced masks has been designed and fabricated to generate high-quality X-ray illumination patterns for use in imaging techniques such as ghost imaging (GI), ghost projection, and speckle tracking. The designs include a range of random binary and orthogonal patterns, fabricated through a combination of photolithography and gold electroplating techniques. We experimentally demonstrated that a single wafer can be used as an illumination mask for GI, employing individual illumination patterns and also a mixture of patterns, using a laboratory X-ray source. The quality of the reconstructed X-ray ghost images has been characterized and evaluated through a range of metrics.

Recovering missing slices of the discrete Fourier transform using Ghosts.

The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n log(2) n) (for an n=N×N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT.

Changes in effective connectivity models in the presence of task-correlated motion: an fMRI study.

We investigated the effects of motion-correction strategy and time course selection method when structural equation modeling is applied to fMRI data in the presence of task-correlated motion. Three motion-correction methods were employed for a group of 12 subjects performing an orthographic lexical retrieval task: (1) a rigid body realignment as implemented in SPM99, (2) a rigid body realignment combined with the inclusion of motion parameters in the statistical model, and (3) the FLIRT motion correction followed by an ICA analysis aiming to identify and remove the motion-related components and the ghosting artifacts. For each motion correction, the time courses of the activated regions were selected in three ways: (1) using the voxels with the highest Z scores, (2) using the average across all the statistically significant voxels in the region of interest, and (3) using a within-region, across-subjects, singular value decomposition. The resulting models of effective connectivity were markedly different, although the activation pattern was not substantially altered by the motion-correction method. Higher values for the path coefficients were obtained for the models fitted to the covariance matrices based on the average time courses than for the covariance matrices based on a single voxel time course. Our results suggest caution with the interpretation of task-induced changes in effective connectivity since, for higher-order cognitive brain functions, multiple models can be fitted to a given data set and these models cannot be rejected on an anatomical or cognitive basis. Hum. Brain Mapping 21:49-63, 2004.

Density of states for vibrations of fractal drums.

Vibrations of membranes with fractal boundaries (fractal drums) are investigated. Numerical results are presented for Koch drums of fractal dimension D(f)=3/2 at prefractal generations 1-3, and for Koch snowflake drums (D(f)=ln 4/ln 3) at generations 3 and 4. The results show that the low-frequency integrated densities of states (IDOS's) of the drums are well approximated by a two-term asymptotic of the form given by the modified Weyl-Berry (MWB) conjecture, which predicts a correction of DeltaN(Omega) proportional, variant Omega(D(f)) to the leading-order Weyl term. In the high-frequency regime, where the half wavelength is smaller than the smallest features of the prefractal perimeter, the two-term Weyl asymptotic is applicable, with DeltaN(Omega) approximately Omega. The results also indicate that oscillations in DeltaN(Omega) arise due to localization of the wave amplitude near the prefractal perimeter. It is argued that for a self-similar fractal boundary, the amplitude of the oscillations is asymptotically proportional to Omega(D(f)), which implies an O(Omega(D(f))), rather than the conjectured o(Omega(D(f))), error term for the asymptotic IDOS given by the MWB conjecture.

Simulation of the effects of global normalization procedures in functional MRI.

We report on differences in sensitivity and false-positive rate across five methods of global normalization using resting-state fMRI data embedded with simulated activation. These methods were grand mean session scaling, proportional scaling, ANCOVA, a masking method, and an orthogonalization method. We found that global normalization by proportional scaling and ANCOVA decreased the sensitivity of the statistical analysis and induced artifactual deactivation even when the correlation between the global signal and the experimental paradigm was relatively low. The masking method and the orthogonalization method performed better from this perspective but are both restricted to certain experimental conditions. Based on the results of these simulations, we offer practical guidelines for the choice of global normalization method least likely to bias the experimental results.