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PurposeTo improve signal-to-noise ratio for diffusion-weighted magnetic resonance images.MethodsA 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.ResultsThe 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.ConclusionThe 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.

Two novel algorithms for the simultaneous estimation of the image and the unknown hyperparameters in total variation (TV)-based image restoration problems are presented. The algorithms provide approximation to the posterior distribution of the latent variables using variational methods.

In this paper, a new algorithm for lossless compression of hyperspectral images is proposed. The spectral redundancy in hyperspectral images is exploited using a context-match method driven by the correlation between adjacent bands. This method is suitable for hyperspectral images in the band-sequential format. Moreover, this method compares favorably with the recent proposed lossless compression algorithms in terms of compression, with a lower complexity. Index Terms--Conditional average, context coding, correlation, entropy code, Golomb-Rice code, hyperspectral image, image coding.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The variational Bayesian (VB) approximation is known to be a promising approach to Bayesian estimation, when the rigorous calculation of the Bayes posterior is intractable. The VB approximation has been successfully applied to matrix factorization (MF), offering automatic dimensionality selection for principal component analysis. Generally, finding the VB solution is a non-convex problem, and most methods rely on a local search algorithm derived through a standard procedure for the VB approximation. In this paper, we show that a better option is available for fully-observed VBMF--the global solution can be analytically computed. More specifically, the global solution is a reweighted SVD of the observed matrix, and each weight can be obtained by solving a quartic equation with its coefficients being functions of the observed singular value. We further show that the global optimal solution of empirical VBMF (where hyperparameters are also learned from data) can also be analytically computed. We illustrate the usefulness of our results through experiments in multi-variate analysis. [ABSTRACT FROM AUTHOR]

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.

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.