PEAR: PEriodic And fixed Rank separation for fast fMRI

In functional MRI (fMRI), faster acquisition via undersampling of data can improve the spatial-temporal resolution trade-off and increase statistical robustness through increased degrees-of-freedom. High quality reconstruction of fMRI data from undersampled measurements requires proper modeling of the data. We present an fMRI reconstruction approach based on modeling the fMRI signal as a sum of periodic and fixed rank components, for improved reconstruction from undersampled measurements. We decompose the fMRI signal into a component which a has fixed rank and a component consisting of a sum of periodic signals which is sparse in the temporal Fourier domain. Data reconstruction is performed by solving a constrained problem that enforces a fixed, moderate rank on one of the components, and a limited number of temporal frequencies on the other. Our approach is coined PEAR - PEriodic And fixed Rank separation for fast fMRI. Experimental results include purely synthetic simulation, a simulation with real timecourses and retrospective undersampling of a real fMRI dataset. Evaluation was performed both quantitatively and visually versus ground truth, comparing PEAR to two additional recent methods for fMRI reconstruction from undersampled measurements. Results demonstrate PEAR's improvement in estimating the timecourses and activation maps versus the methods compared against at acceleration ratios of R=8,16 (for simulated data) and R=6.66,10 (for real data). PEAR results in reconstruction with higher fidelity than when using a fixed-rank based model or a conventional Low-rank+Sparse algorithm. We have shown that splitting the functional information between the components leads to better modeling of fMRI, over state-of-the-art methods

Appendix

Table.1a. Patient’s Demographic and Clinical Characteristics. Table.1b. Screening Criteria. Fig.1. CONSORT Flow Diagram. Fig.2. ROIs Constructing The Chronic Pain Matrix Used For Graph Theory Analysis. Fig.3. Adjacency Matrix Threshol

Joint Multicontrast MRI Reconstruction

Joint reconstruction is relevant for a variety of medical imaging applications, where multiple images are acquired in parallel or within a single scanning procedure. Examples include joint reconstruction of different medical imaging modalities (e.g. CT and PET) and various MRI applications (e.g. different MR imaging contrasts of the same patient). In this paper we present an approach for joint reconstruction of two MR images, based on partial sampling of both. We assume each MR image has a limited number of edges, that is, low total variation, but they are similar in the sense that many of the edges overlap. We examine synthetic phantoms representing T1 and T2 imaging contrasts and realistic T1-weighted and T2-weighted images of the same patient. We show that our joint reconstruction approach outperforms conventional TV-based MRI reconstruction for each image solely. Results are shown both visually and numerically for sampling ratios of 4%-20%, and consist of an improvement of up to 3.6dB

Reference-based compressed sensing:A sample complexity approach

We address the problem of reference-based compressed sensing: reconstruct a sparse signal from few linear measurements using as prior information a reference signal, a signal similar to the signal we want to reconstruct. Access to reference signals arises in applications such as medical imaging, e.g., through prior images of the same patient, and compressive video, where previously reconstructed frames can be used as reference. Our goal is to use the reference signal to reduce the number of required measurements for reconstruction. We achieve this via a reweighted ℓ1-ℓ1 minimization scheme that updates its weights based on a sample complexity bound. The scheme is simple, intuitive and, as our experiments show, outperforms prior algorithms, including reweighted ℓ1 minimization, ℓ1-ℓ1 minimization, and modified CS