Weihong Guo

A New Detail-Preserving Regularization Scheme

It is a challenging task to reconstruct images from their noisy, blurry, and/or incomplete measurements, especially those with important details and features such as medical magnetic resonance (MR) and CT images. We propose a novel regularization model that integrates two recently developed regularization tools: total generalized variation (TGV) by Bredies, Kunisch, and Pock; and shearlet transform by Labate, Lim, Kutyniok, and Weiss. The proposed model recovers both edges and fine details of images much better than the existing regularization models based on the total variation (TV) and wavelets. Specifically, while TV preserves sharp edges but suffers from oil painting artifacts, TGV “selectively regularizes” different image regions at different levels and thus largely avoids oil painting artifacts. Unlike the wavelet transform, which represents isotropic image features much more sparsely than anisotropic ones, the shearlet transform can efficiently represent anisotropic features such as edges, curves, ...

A rapid and robust numerical algorithm for sensitivity encoding with sparsity constraints: self-feeding sparse SENSE.

The method of enforcing sparsity during magnetic resonance imaging reconstruction has been successfully applied to partially parallel imaging (PPI) techniques to reduce noise and artifact levels and hence to achieve even higher acceleration factors. However, there are two major problems in the existing sparsity‐constrained PPI techniques: speed and robustness. By introducing an auxiliary variable and decomposing the original minimization problem into two subproblems that are much easier to solve, a fast and robust numerical algorithm for sparsity‐constrained PPI technique is developed in this work. The specific implementation for a conventional Cartesian trajectory data set is named self‐feeding Sparse Sensitivity Encoding (SENSE). The computational cost for the proposed method is two conventional SENSE reconstructions plus one spatially adaptive image denoising procedure. With reconstruction time approximately doubled, images with a much lower root mean square error (RMSE) can be achieved at high acceleration factors. Using a standard eight‐channel head coil, a net acceleration factor of 5 along one dimension can be achieved with low RMSE. Furthermore, the algorithm is insensitive to the choice of parameters. This work improves the clinical applicability of SENSE at high acceleration factors. Magn Reson Med, 2010.

EdgeCS: Edge Guided Compressive Sensing Reconstruction

Compressive sensing (CS) reconstructs images from a small number of projections. We propose EdgeCS - edge guided CS reconstruction - to recover images of higher qualities from fewer measurements than the current state-of-the-art methods. Accurate edge information can significantly improve image recovery quality and speed, but such information is encoded in the CS measurements of an image. To take advantage of edge information in CS recovery, EdgeCS alternatively performs CS reconstruction and edge detection in a way that each benefits from the latest solution of the other. EdgeCS is fast and returns high-quality images. It exactly recovers the 256 × 256 Shepp-Logan phantom from merely 7 radial lines (or 3.03% k-space), which is impossible for most existing algorithms. It accurately reconstructs a 512 × 512 magnetic resonance image from 21% noisy samples. Moreover, it is also able to reconstruct complex-valued images. Each took about 30 seconds on an ordinary laptop. The algorithm can be easily ported to GPUs for a speedup of more than 10 folds.

Edge Guided Reconstruction for Compressive Imaging

We propose EdgeCS---an edge guided compressive sensing reconstruction approach---to recover images of higher quality from fewer measurements than the current methods. Edges are important image features that are used in various ways in image recovery, analysis, and understanding. In compressive sensing, the sparsity of image edges has been successfully utilized to recover images. However, edge detectors have not been used on compressive sensing measurements to improve the edge recovery and subsequently the image recovery. This motivates us to propose EdgeCS, which alternatively performs edge detection and image reconstruction in a mutually beneficial way. The edge detector of EdgeCS is designed to faithfully return partial edges from intermediate image reconstructions even though these reconstructions may still have noise and artifacts. For complex-valued images, it incorporates joint sparsity between the real and imaginary components. EdgeCS has been implemented with both isotropic and anisotropic discret...

Estimation, smoothing, and characterization of apparent diffusion coefficient profiles from High Angular Resolution DWI

We present a new variational framework for recovery of apparent diffusion coefficient (ADC)from High Angular Resolution Diffusion-weighted (HARD) MRI. The model approximates the ADC profiles by a 4th order spherical harmonic series (SHS), whose coefficients are obtained by solving a constrained minimization problem. By minimizing the energy functional, the ADC profiles are estimated and regularized simultaneously across the entire volume. In this model, feature preserving smoothing is achieved by minimizing a non-standard growth functional, and the estimation is based on the original Stejskal-Tanner equation. The antipodal symmetry and positiveness of the ADC are also accommodated into the model. Furthermore, coefficients of the SHS and the variance of ADC profiles from its mean are used to characterize the diffusion anisotropy. The effectiveness of the proposed model is depicted via application to both simulated and HARD MRI human brain data. The characterization of non-Gaussian diffusion based on the proposed model showed consistency with known neuroanatomy.

Using multiple tensor deflection to reconstruct white matter fiber traces with branching

The relationship between brain structure and complex behavior is governed by large-scale neurocognitive networks. Diffusion weighted imaging (DWI) is a noninvasive technique that can visualize the neuronal projections connecting the functional centers and thus provides new keys to the understanding of brain function. In this paper, we assume there are up to two diffusion channels at each voxel. A variational framework for 3D simultaneous smoothing and reconstruction of a multi-diffusion tensor field as well as a novel multi-tensor deflection (MTEND) algorithm for extracting white matter fiber traces based on the multi-diffusion tensor field are provided. By applying the proposed model to both synthetic data and human brain high angular resolution diffusion (HARD) magnetic resonance imaging (MRI) data of several subjects, we show the effectiveness of the model in recovering branching fiber traces. Superiority of the proposed model over existing models are also demonstrated

Apparent diffusion coefficient approximation and diffusion anisotropy characterization in DWI

We present a new approximation for the apparent diffusion coefficient (ADC) of non-Gaussian water diffusion with at most two fiber orientations within a voxel. The proposed model approximates ADC profiles by product of two spherical harmonic series (SHS) up to order 2 from High Angular Resolution Diffusion-weighted (HARD) MRI data. The coefficients of SHS are estimated and regularized simultaneously by solving a constrained minimization problem. An equivalent but non-constrained version of the approach is also provided to reduce the complexity and increase the efficiency in computation. Moreover we use the Cumulative Residual Entropy (CRE) as a measurement to characterize diffusion anisotropy. By using CRE we can get reasonable results with two thresholds, while the existing methods either can only be used to characterize Gaussian diffusion or need more measurements and thresholds to classify anisotropic diffusion with two fiber orientations. The experiments on HARD MRI human brain data indicate the effectiveness of the method in the recovery of ADC profiles. The characterization of diffusion based on the proposed method shows a consistency between our results and known neuroanatomy.

Adaptive total variation based filtering for MRI images with spatially inhomogeneous noise and artifacts

The widely adopted total variation (TV) filter is not optimal for MRI images with spatially varying noise levels, not to say those with also artifacts. To better preserve edges and fine structures while sufficiently removing noise and artifacts, we first use local mutual information together with k-means segmentation to automatically locate most of the reliable edges from the noisy input; noise and artifacts distribution at other regions are then studied using local variance; all obtained transparent information in turn guides fully automatic local adjustment of the TV filter. The proposed spatially adaptive TV model has been applied to partially parallel MRI (PP-MRI) image reconstructed using GRAPPA and SENSE. Comparison with Perona-Malik anisotropic diffusion and another adaptive TV verifies that the proposed model provides higher peak signal to noise ratio (PSNR) and results closer to ground truth. Numerical results on many in vivo clinical data sets demonstrate the robustness and viability of the unsupervised method.

A Local Mutual Information Guided Denoising Technique and Its Application to Self-calibrated Partially Parallel Imaging

The application of Partially Parallel Imaging (PPI) techniques to regular clinical Magnetic Resonance Imaging (MRI) studies has brought about the benefit of significantly faster acquisitions but at the cost of amplified and spatially variant noise, especially, for high parallel imaging acceleration rates. A Local Mutual Information (LMI) weighted Total Variation (TV) based model is proposed to remove non-evenly distributed noise while preserving image sharpness. For self-calibrated PPI, such as GeneRalized Auto-calibration Partially Parallel Acquisition (GRAPPA) and modified SENSitivity Encoding (mSENSE), a low spatial resolution high Signal to Noise Ratio (SNR) image is available besides the reconstructed high spatial resolution low SNR image. The LMI between these two images is used to detect the noise distribution and the location of edges automatically, and is then applied as guidance for denoising. To better preserve sharpness, Bregman iteration scheme is utilized to add the removed signal back to the denoised image. Entropy of the residual map is used to automatically terminate iteration without using any information of the golden standard or real noise. Results of the proposed algorithm on synthetic and in vivo MR images indicate that the proposed technique preserves image edges and suppresses noise well in the images reconstructed by GRAPPA. The comparison with some existing techniques further confirms the advantages. This algorithm can be applied to enhance the clinical applicability of self-calibrated PPI. Potentially, it can be extended to denoise general images with spatially variant noise.

Using Prior Shape and Points in Medical Image Segmentation

In this paper we present a new variational framework in level set form for image segmentation, which incorporates both a prior shape and prior fixed locations of a small number of points. The idea underlying the model is the creation of two energy terms in the energy function for the geodesic active contours. The first energy term is for the shape, the second for the locations of the points In this model, segmentation is achieved through a registration technique, which combines a rigid transformation and a local deformation. The rigid transformation is determined explicitly by using shape information, while the local deformation is determined implicitly by using image gradients and prior locations. We report experimental results on both synthetic and ultrasound images. These results compared with the results obtained by using a previously reported model, which only incorporates a shape prior into the active contours.