Denoising diffusion-weighted magnitude MR images using rank and edge constraints.

PURPOSE: To improve signal-to-noise ratio for diffusion-weighted magnetic resonance images. METHODS: A new method is proposed for denoising diffusion-weighted magnitude images. The proposed method formulates the denoising problem as an maximum a posteriori} estimation problem based on Rician/noncentral χ likelihood models, incorporating an edge prior and a low-rank model. The resulting optimization problem is solved efficiently using a half-quadratic method with an alternating minimization scheme. RESULTS: The performance of the proposed method has been validated using simulated and experimental data. Diffusion-weighted images and noisy data were simulated based on the diffusion tensor imaging model and Rician/noncentral χ distributions. The simulation study (with known gold standard) shows substantial improvements in single-to-noise ratio and diffusion tensor estimation after denoising. In vivo diffusion imaging data at different b-values were acquired. Based on the experimental data, qualitative improvement in image quality and quantitative improvement in diffusion tensor estimation were demonstrated. Additionally, the proposed method is shown to outperform one of the state-of-the-art nonlocal means-based denoising algorithms, both qualitatively and quantitatively. CONCLUSION: The single-to-noise ratio of diffusion-weighted images can be effectively improved with rank and edge constraints, resulting in an improvement in diffusion parameter estimation accuracy.

Bayesian symmetrical EEG/fMRI fusion with spatially adaptive priors.

In this paper, we propose a novel symmetrical EEG/fMRI fusion method which combines EEG and fMRI by means of a common generative model. We use a total variation (TV) prior to model the spatial distribution of the cortical current responses and hemodynamic response functions, and utilize spatially adaptive temporal priors to model their temporal shapes. The spatial adaptivity of the prior model allows for adaptation to the local characteristics of the estimated responses and leads to high estimation performance for the cortical current distribution and the hemodynamic response functions. We utilize a Bayesian formulation with a variational Bayesian framework and obtain a fully automatic fusion algorithm. Simulations with synthetic data and experiments with real data from a multimodal study on face perception demonstrate the performance of the proposed method.

Variational bayesian blind deconvolution using a total variation prior.

In this paper, we present novel algorithms for total variation (TV) based blind deconvolution and parameter estimation utilizing a variational framework. Using a hierarchical Bayesian model, the unknown image, blur, and hyperparameters for the image, blur, and noise priors are estimated simultaneously. A variational inference approach is utilized so that approximations of the posterior distributions of the unknowns are obtained, thus providing a measure of the uncertainty of the estimates. Experimental results demonstrate that the proposed approaches provide higher restoration performance than non-TV-based methods without any assumptions about the unknown hyperparameters.

Parameter estimation in TV image restoration using variational distribution approximation.

In this paper, we propose novel algorithms for total variation (TV) based image restoration and parameter estimation utilizing variational distribution approximations. Within the hierarchical Bayesian formulation, the reconstructed image and the unknown hyper parameters for the image prior and the noise are simultaneously estimated. The proposed algorithms provide approximations to the posterior distributions of the latent variables using variational methods. We show that some of the current approaches to TV-based image restoration are special cases of our framework. Experimental results show that the proposed approaches provide competitive performance without any assumptions about unknown hyper parameters and clearly outperform existing methods when additional information is included.

Variational Bayesian causal connectivity analysis for fMRI.

The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience. We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data. The method uses a vector autoregressive model for the latent variables describing neuronal activity in combination with a linear observation model based on a convolution with a hemodynamic response function. Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm. The computational efficiency of the method enables us to apply it to large scale problems with high sampling rates and several hundred regions of interest. We use a comprehensive empirical evaluation with synthetic and real fMRI data to evaluate the performance of our method under various conditions.

ACCELERATING CARDIOVASCULAR IMAGING BY EXPLOITING REGIONAL LOW-RANK STRUCTURE VIA GROUP SPARSITY.

Sparse sampling of (k, t)-space has proved useful for cardiac MRI. This paper builds on previous work on using partial separability (PS) and spatial-spectral sparsity for high-quality image reconstruction from highly undersampled (k, t)-space data. This new method uses a more flexible control over the PS-induced low-rank constraint via group-sparse regularization. A novel algorithm is also described to solve the corresponding (1,2)-norm regularized inverse problem. Reconstruction results from simulated cardiovascular imaging data are presented to demonstrate the performance of the proposed method.

Visualizing Escherichia coli sub-cellular structure using sparse deconvolution Spatial Light Interference Tomography.

Studying the 3D sub-cellular structure of living cells is essential to our understanding of biological function. However, tomographic imaging of live cells is challenging mainly because they are transparent, i.e., weakly scattering structures. Therefore, this type of imaging has been implemented largely using fluorescence techniques. While confocal fluorescence imaging is a common approach to achieve sectioning, it requires fluorescence probes that are often harmful to the living specimen. On the other hand, by using the intrinsic contrast of the structures it is possible to study living cells in a non-invasive manner. One method that provides high-resolution quantitative information about nanoscale structures is a broadband interferometric technique known as Spatial Light Interference Microscopy (SLIM). In addition to rendering quantitative phase information, when combined with a high numerical aperture objective, SLIM also provides excellent depth sectioning capabilities. However, like in all linear optical systems, SLIM's resolution is limited by diffraction. Here we present a novel 3D field deconvolution algorithm that exploits the sparsity of phase images and renders images with resolution beyond the diffraction limit. We employ this label-free method, called deconvolution Spatial Light Interference Tomography (dSLIT), to visualize coiled sub-cellular structures in E. coli cells which are most likely the cytoskeletal MreB protein and the division site regulating MinCDE proteins. Previously these structures have only been observed using specialized strains and plasmids and fluorescence techniques. Our results indicate that dSLIT can be employed to study such structures in a practical and non-invasive manner.

Compressive light field sensing.

We propose a novel design for light field image acquisition based on compressive sensing principles. By placing a randomly coded mask at the aperture of a camera, incoherent measurements of the light passing through different parts of the lens are encoded in the captured images. Each captured image is a random linear combination of different angular views of a scene. The encoded images are then used to recover the original light field image via a novel Bayesian reconstruction algorithm. Using the principles of compressive sensing, we show that light field images with a large number of angular views can be recovered from only a few acquisitions. Moreover, the proposed acquisition and recovery method provides light field images with high spatial resolution and signal-to-noise-ratio, and therefore is not affected by limitations common to existing light field camera designs. We present a prototype camera design based on the proposed framework by modifying a regular digital camera. Finally, we demonstrate the effectiveness of the proposed system using experimental results with both synthetic and real images.

Variational bayesian super resolution.

In this paper, we address the super resolution (SR) problem from a set of degraded low resolution (LR) images to obtain a high resolution (HR) image. Accurate estimation of the sub-pixel motion between the LR images significantly affects the performance of the reconstructed HR image. In this paper, we propose novel super resolution methods where the HR image and the motion parameters are estimated simultaneously. Utilizing a bayesian formulation, we model the unknown HR image, the acquisition process, the motion parameters and the unknown model parameters in a stochastic sense. Employing a variational bayesian analysis, we develop two novel algorithms which jointly estimate the distributions of all unknowns. The proposed framework has the following advantages: 1) Through the incorporation of uncertainty of the estimates, the algorithms prevent the propagation of errors between the estimates of the various unknowns; 2) the algorithms are robust to errors in the estimation of the motion parameters; and 3) using a fully bayesian formulation, the developed algorithms simultaneously estimate all algorithmic parameters along with the HR image and motion parameters, and therefore they are fully-automated and do not require parameter tuning. We also show that the proposed motion estimation method is a stochastic generalization of the classical Lucas-Kanade registration algorithm. Experimental results demonstrate that the proposed approaches are very effective and compare favorably to state-of-the-art SR algorithms.

Cell imaging beyond the diffraction limit using sparse deconvolution spatial light interference microscopy.

We present an imaging method, dSLIM, that combines a novel deconvolution algorithm with spatial light interference microscopy (SLIM), to achieve 2.3x resolution enhancement with respect to the diffraction limit. By exploiting the sparsity of the phase images, which is prominent in many biological imaging applications, and modeling of the image formation via complex fields, the very fine structures can be recovered which were blurred by the optics. With experiments on SLIM images, we demonstrate that significant improvements in spatial resolution can be obtained by the proposed approach. Moreover, the resolution improvement leads to higher accuracy in monitoring dynamic activity over time. Experiments with primary brain cells, i.e. neurons and glial cells, reveal new subdiffraction structures and motions. This new information can be used for studying vesicle transport in neurons, which may shed light on dynamic cell functioning. Finally, the method is flexible to incorporate a wide range of image models for different applications and can be utilized for all imaging modalities acquiring complex field images.

Reference-guided sparsifying transform design for compressive sensing MRI.

Compressive sensing (CS) MRI aims to accurately reconstruct images from undersampled k-space data. Most CS methods employ analytical sparsifying transforms such as total-variation and wavelets to model the unknown image and constrain the solution space during reconstruction. Recently, nonparametric dictionary-based methods for CS-MRI reconstruction have shown significant improvements over the classical methods. These existing techniques focus on learning the representation basis for the unknown image for a synthesis-based reconstruction. In this paper, we present a new framework for analysis-based reconstruction, where the sparsifying transform is learnt from a reference image to capture the anatomical structure of unknown image, and is used to guide the reconstruction process. We demonstrate with experimental data the high performance of the proposed approach over traditional methods.

Bayesian compressive sensing using laplace priors.

In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation, and, therefore, no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1-D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.

INTERVENTIONAL MRI WITH SPARSE SAMPLING USING UNION-OF-SUBSPACES.

A significant problem in interventional magnetic resonance imaging is limited imaging speed. This paper addresses this problem using a new signal model known as union-of-subspaces. This model enables an effective use of sparse sampling and prior information to significantly improve the imaging speed. The proposed method has been validated using simulations on real interventional imaging data, and is shown to provide high speed and quality imaging. The approach is very flexible and can be applied to other imaging applications as well.