Wenxing Ye

A Geometric Construction of Multivariate Sinc Functions

We present a geometric framework for explicit derivation of multivariate sampling functions (sinc) on multidimensional lattices. The approach leads to a generalization of the link between sinc functions and the Lagrange interpolation in the multivariate setting. Our geometric approach also provides a frequency partition of the spectrum that leads to a nonseparable extension of the 1-D Shannon (sinc) wavelets to the multivariate setting. Moreover, we propose a generalization of the Lanczos window function that provides a practical and unbiased approach for signal reconstruction on sampling lattices. While this framework is general for lattices of any dimension, we specifically characterize all 2-D and 3-D lattices and show the detailed derivations for 2-D hexagonal body-centered cubic (BCC) and face-centered cubic (FCC) lattices. Both visual and numerical comparisons validate the theoretical expectations about superiority of the BCC and FCC lattices over the commonly used Cartesian lattice.

An Efficient Interlaced Multi-Shell Sampling Scheme for Reconstruction of Diffusion Propagators

In this paper, we propose an interlaced multi-shell sampling scheme for the reconstruction of the diffusion propagator from diffusion weighted magnetic resonance imaging (DW-MRI). In standard multi-shell sampling schemes, sample points are uniformly distributed on several spherical shells in q-space. The distribution of sample points is the same for all shells, and is determined by the vertices of a selected polyhedron. We propose a more efficient interlaced scheme where sample points are different on alternating shells and are determined by the vertices of a pair of dual polyhedra. Since it samples more directions than the standard scheme, this method offers increased angular discrimination. Another contribution of this work is the application of optimal sampling lattices to q-space data acquisition and the proposal of a model-free reconstruction algorithm, which uses the lattice dependent sinc interpolation function. It is shown that under this reconstruction framework, the body centered cubic (BCC) lattice provides increased accuracy. The sampling scheme and the reconstruction algorithms were evaluated on simulated data as well as rat brain data collected on a 600 MHz (14.1T) Bruker imaging spectrometer.

An over-complete dictionary based regularized reconstruction of a field of ensemble average propagators

In this paper we present a dictionary-based framework for the reconstruction of a field of ensemble average propagators (EAPs), given a high angular resolution diffusion MRI data set. Existing techniques often consider voxel-wise reconstruction of the EAP field thereby leading to a noisy reconstruction across the field. We present a dictionary learning framework for achieving a smooth EAP reconstruction across the field wherein, the dictionary atoms are learned from the data via an initial regression using adaptive spline kernels. The formulation involves a two stage optimization where the first stage involves optimizing for a sparse dictionary using a K-SVD based updating and the second stage involves a quadratic cost function optimization with a non-local means based regularization across the field. The novelty lies in a dictionary based reconstruction as well as an NLM-based regularization that helps preserving features in the reconstructed field. We document experimental results on synthetic data from crossing fibers and real optic chiasm data set that demonstrate the advantages of the proposed approach.

Bandlimited Reconstruction of Multidimensional Images From Irregular Samples

We examine different sampling lattices and their respective bandlimited spaces for reconstruction of irregularly sampled multidimensional images. Considering an irregularly sampled dataset, we demonstrate that the non-tensor-product bandlimited approximations corresponding to the body-centered cubic and face-centered cubic lattices provide a more accurate reconstruction than the tensor-product bandlimited approximation associated with the commonly-used Cartesian lattice. Our practical algorithm uses multidimensional sinc functions that are tailored to these lattices and a regularization scheme that provides a variational framework for efficient implementation. Using a number of synthetic and real data sets we record improvements in the accuracy of reconstruction in a practical setting.

Box spline based 3D tomographic reconstruction of diffusion propagators from MRI data

This paper introduces a tomographic approach for reconstruction of diffusion propagators, P(r), in a box spline framework. Box splines are chosen as basis functions for highorder approximation of P(r) from the diffusion signal. Box splines are a generalization of B-splines to multivariate setting that are particularly useful in the context of tomographic reconstruction. The X-Ray or Radon transform of a (tensorproduct B-spline or a non-separable) box spline is a box spline - the space of box splines is closed under the Radon transform. We present synthetic and real multi-shell diffusionweighted MR data experiments that demonstrate the increased accuracy of P(r) reconstruction as the order of basis functions is increased.

Tomographic reconstruction of diffusion propagators from DW-MRI using optimal sampling lattices

This paper exploits the power of optimal sampling lattices in tomography based reconstruction of the diffusion propagator in diffusion weighted magnetic resonance imaging (DW-MRI). Optimal sampling leads to increased accuracy of the tomographic reconstruction approach introduced by Pickalov and Basser [1]. Alternatively, the optimal sampling geometry allows for further reducing the number of samples while maintaining the accuracy of reconstruction of the diffusion propagator. The optimality of the proposed sampling geometry comes from the information theoretic advantages of sphere packing lattices in sampling multidimensional signals. These advantages are in addition to those accrued from the use of the tomographic principle used here for reconstruction. We present comparative results of reconstructions of the diffusion propagator using the Cartesian and the optimal sampling geometry for synthetic and real data sets.

A rotation-invariant transform for target detection in SAR images

Rotation of targets pose great a challenge for the design of an automatic image-based target detection system. In this paper, we propose a target detection algorithm that is robust to rotation of targets. Our key idea is to use rotation invariant features as the input for the classifier. For an image in Radon transform space, namely R(b,θ), taking the magnitude of 1-D Fourier transform on θ, we get |Fθ{R(b,θ)}|. It was proved that the coefficients of the combined Radon and 1-D Fourier transform, |Fθ{R(b,θ)}| is invariant to rotation of the image. These coefficients are used as the input to a maximum-margin classifier based on I-RELIEF feature weighting technique. Its objective is to maximize the margin between two classes and improve the robustness of the classifier against uncertainties. For each pixel of a sample SAR image, a feature vector can be extracted from a sub image centered at that pixel. Then our classifier decides whether the pixel is target or non-target. This produces a binary-valued image. We further improve the detection performance by connectivity analysis, image differencing and diversity combining. We evaluate the performance of our proposed algorithm, using the data set collected by Swedish CARABAS-II systems, and the experimental results show that our proposed algorithm achieves superior performance over the benchmark algorithm.

Design of bivariate sinc wavelets

This paper introduces a new way of constructing 2-D wavelets which generalizes the univariate sinc wavelets to images sampled on arbitrary lattices. For lattices other than Cartesian, such wavelets are no longer tensor products of the univariate version. The proposed construction method is based on the zonotope decomposition of the Brillouin zone of the lattice and can be generalized to all 2-D or 3-D lattices. While our construction allows for the derivation of sinc wavelets for any 2-D lattice, we particularly study the case for the hexagonal lattice. We present experiments that contrast Cartesian tensor-product wavelet decomposition against the non-separable hexagonal wavelet decomposition and demonstrate the increased isotropy in the latter case.

A target detection scheme for VHF SAR ground surveillance

Detection of targets concealed in foliage is a challenging problem and is critical for ground surveillance. To detect foliage-concealed targets, we need to address two major challenges, namely, 1) how to remotely acquire information that contains important features of foliage-concealed targets, and 2) how to distinguish targets from background and clutter. Synthetic aperture radar operated in low VHF-band has shown very good penetration capability in the forest environment, and hence the first problem can be satisfactorily addressed. The second problem is the focus of this paper. Existing detection schemes can achieve good detection performance but at the cost of high false alarm rate. To address the limitation of the existing schemes, in this paper, we develop a target detection algorithm based on a supervised learning technique that maximizes the margin between two classes, i.e., the target class and the non-target class. Specifically, our target detection algorithm consists of 1) image differencing, 2) maximum-margin classifier, and 3) diversity combining. The image differencing is to enhance and highlight the targets so that the targets are more distinguishable from the background. The maximum-margin classifier is based on a recently developed feature weighting technique called I-RELIEF; the objective of the maximum-margin classifier is to achieve robustness against uncertainties and clutter. The diversity combining utilizes multiple images to further improve the performance of detection, and hence it is a type of multi-pass change detection. We evaluate the performance of our proposed detection algorithm, using the SAR image data collected by Swedish CARABAS-II systems which operates at low VHF-band around 20-90 MHz. The experimental results demonstrate superior performance of our algorithm, compared to the benchmark algorithm associated with the CARABAS-II SAR image data. For example, for the same level of target detection probability, our algorithm only produces 11 false alarms while the benchmark algorithm produces 86 false alarms.