Sparse Reconstruction of Compressive Sensing MRI using Cross-Domain Stochastically Fully Connected Conditional Random Fields

Magnetic Resonance Imaging (MRI) is a crucial medical imaging technology for the screening and diagnosis of frequently occurring cancers. However image quality may suffer by long acquisition times for MRIs due to patient motion, as well as result in great patient discomfort. Reducing MRI acquisition time can reduce patient discomfort and as a result reduces motion artifacts from the acquisition process. Compressive sensing strategies, when applied to MRI, have been demonstrated to be effective at decreasing acquisition times significantly by sparsely sampling the \emph{k}-space during the acquisition process. However, such a strategy requires advanced reconstruction algorithms to produce high quality and reliable images from compressive sensing MRI. This paper proposes a new reconstruction approach based on cross-domain stochastically fully connected conditional random fields (CD-SFCRF) for compressive sensing MRI. The CD-SFCRF introduces constraints in both \emph{k}-space and spatial domains within a stochastically fully connected graphical model to produce improved MRI reconstruction. Experimental results using T2-weighted (T2w) imaging and diffusion-weighted imaging (DWI) of the prostate show strong performance in preserving fine details and tissue structures in the reconstructed images when compared to other tested methods even at low sampling rates.Comment: 9 page

Projected Iterative Soft-thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging

Compressed sensing has shown great potentials in accelerating magnetic resonance imaging. Fast image reconstruction and high image quality are two main issues faced by this new technology. It has been shown that, redundant image representations, e.g. tight frames, can significantly improve the image quality. But how to efficiently solve the reconstruction problem with these redundant representation systems is still challenging. This paper attempts to address the problem of applying iterative soft-thresholding algorithm (ISTA) to tight frames based magnetic resonance image reconstruction. By introducing the canonical dual frame to construct the orthogonal projection operator on the range of the analysis sparsity operator, we propose a projected iterative soft-thresholding algorithm (pISTA) and further accelerate it by incorporating the strategy proposed by Beck and Teboulle in 2009. We theoretically prove that pISTA converges to the minimum of a function with a balanced tight frame sparsity. Experimental results demonstrate that the proposed algorithm achieves better reconstruction than the widely used synthesis sparse model and the accelerated pISTA converges faster or comparable to the state-of-art smoothing FISTA. One major advantage of pISTA is that only one extra parameter, the step size, is introduced and the numerical solution is stable to it in terms of image reconstruction errors, thus allowing easily setting in many fast magnetic resonance imaging applications.Comment: 10 pages, 10 figure

Fast Multi-class Dictionaries Learning with Geometrical Directions in MRI Reconstruction

Objective: Improve the reconstructed image with fast and multi-class dictionaries learning when magnetic resonance imaging is accelerated by undersampling the k-space data. Methods: A fast orthogonal dictionary learning method is introduced into magnetic resonance image reconstruction to providing adaptive sparse representation of images. To enhance the sparsity, image is divided into classified patches according to the same geometrical direction and dictionary is trained within each class. A new sparse reconstruction model with the multi-class dictionaries is proposed and solved using a fast alternating direction method of multipliers. Results: Experiments on phantom and brain imaging data with acceleration factor up to 10 and various undersampling patterns are conducted. The proposed method is compared with state-of-the-art magnetic resonance image reconstruction methods. Conclusion: Artifacts are better suppressed and image edges are better preserved than the compared methods. Besides, the computation of the proposed approach is much faster than the typical K-SVD dictionary learning method in magnetic resonance image reconstruction. Significance: The proposed method can be exploited in undersapmled magnetic resonance imaging to reduce data acquisition time and reconstruct images with better image quality.Comment: 13 pages, 15 figures, 5 table

On some common compressive sensing recovery algorithms and applications - Review paper

Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy with significantly reduced number of samples needed for accurate signal reconstruction. The basic ideas and motivation behind this approach are provided in the theoretical part of the paper. The commonly used algorithms for missing data reconstruction are presented. The Compressive Sensing applications have gained significant attention leading to an intensive growth of signal processing possibilities. Hence, some of the existing practical applications assuming different types of signals in real-world scenarios are described and analyzed as well.Comment: submitted to Facta Universitatis Scientific Journal, Series: Electronics and Energetics, March 201

Optimization methods for MR image reconstruction (long version)

The development of compressed sensing methods for magnetic resonance (MR) image reconstruction led to an explosion of research on models and optimization algorithms for MR imaging (MRI). Roughly 10 years after such methods first appeared in the MRI literature, the U.S. Food and Drug Administration (FDA) approved certain compressed sensing methods for commercial use, making compressed sensing a clinical success story for MRI. This review paper summarizes several key models and optimization algorithms for MR image reconstruction, including both the type of methods that have FDA approval for clinical use, as well as more recent methods being considered in the research community that use data-adaptive regularizers. Many algorithms have been devised that exploit the structure of the system model and regularizers used in MRI; this paper strives to collect such algorithms in a single survey. Many of the ideas used in optimization methods for MRI are also useful for solving other inverse problems.Comment: Extended (and revised) version of invited paper submitted to IEEE SPMag special issue on "Computational MRI: Compressed Sensing and Beyond.

Data-Driven Learning of a Union of Sparsifying Transforms Model for Blind Compressed Sensing

Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying sparse signal model is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly undersampled measurements. Specifically, our model is that the patches of the underlying image(s) are approximately sparse in a transform domain. We also extend this model to a union of transforms model that better captures the diversity of features in natural images. The proposed block coordinate descent type algorithms for blind compressed sensing are highly efficient, and are guaranteed to converge to at least the partial global and partial local minimizers of the highly non-convex BCS problems. Our numerical experiments show that the proposed framework usually leads to better quality of image reconstructions in MRI compared to several recent image reconstruction methods. Importantly, the learning of a union of sparsifying transforms leads to better image reconstructions than a single adaptive transform.Comment: Appears in IEEE Transactions on Computational Imaging, 201

Bayesian Nonparametric Dictionary Learning for Compressed Sensing MRI

We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and the patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov Chain Monte Carlo (MCMC) for the Bayesian model, and use the alternating direction method of multipliers (ADMM) for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods

Denoising Auto-encoding Priors in Undecimated Wavelet Domain for MR Image Reconstruction

Compressive sensing is an impressive approach for fast MRI. It aims at reconstructing MR image using only a few under-sampled data in k-space, enhancing the efficiency of the data acquisition. In this study, we propose to learn priors based on undecimated wavelet transform and an iterative image reconstruction algorithm. At the stage of prior learning, transformed feature images obtained by undecimated wavelet transform are stacked as an input of denoising autoencoder network (DAE). The highly redundant and multi-scale input enables the correlation of feature images at different channels, which allows a robust network-driven prior. At the iterative reconstruction, the transformed DAE prior is incorporated into the classical iterative procedure by the means of proximal gradient algorithm. Experimental comparisons on different sampling trajectories and ratios validated the great potential of the presented algorithm.Comment: 10 pages, 11 figures, 6 table

Structurally Adaptive Multi-Derivative Regularization for Image Recovery from Sparse Fourier Samples

The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction, magnetic resonance imaging, and so on. Originally, the primary role of the regularization was to stabilize the computational inversion of the imaging forward model against noise. However, a recent framework pioneered by Donoho and others, known as compressive sensing, brought the role of regularization beyond the stabilization of inversion. It established a possibility that regularization can recover full images from highly undersampled measurements. However, it was observed that the quality of reconstruction yielded by compressive sensing methods falls abruptly when the under-sampling and/or measurement noise goes beyond a certain threshold. Recently developed learning-based methods are believed to outperform the compressive sensing methods without a steep drop in the reconstruction quality under such imaging conditions. However, the need for training data limits their applicability. In this paper, we develop a regularization method that outperforms compressive sensing methods as well as selected learning-based methods, without any need for training data. The regularization is constructed as a spatially varying weighted sum of first- and canonical second-order derivatives, with the weights determined to be adaptive to the image structure; the weights are determined such that the attenuation of sharp image features -- which is inevitable with the use of any regularization -- is significantly reduced. We demonstrate the effectiveness of the proposed method by performing reconstruction on sparse Fourier samples simulated from a variety of MRI images

Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems

The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speed-ups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction.Comment: Accepted to IEEE Transactions on Computational Imaging. This paper also cites experimental results reported in arXiv:1511.0884