Sunrita Poddar

Dynamic MRI Using SmooThness Regularization on Manifolds (SToRM)

We introduce a novel algorithm to recover real time dynamic MR images from highly under-sampled k- t space measurements. The proposed scheme models the images in the dynamic dataset as points on a smooth, low dimensional manifold in high dimensional space. We propose to exploit the non-linear and non-local redundancies in the dataset by posing its recovery as a manifold smoothness regularized optimization problem. A navigator acquisition scheme is used to determine the structure of the manifold, or equivalently the associated graph Laplacian matrix. The estimated Laplacian matrix is used to recover the dataset from undersampled measurements. The utility of the proposed scheme is demonstrated by comparisons with state of the art methods in multi-slice real-time cardiac and speech imaging applications.

Joint recovery of under sampled signals on a manifold: Application to free breathing cardiac MRI

We introduce novel algorithms for the joint recovery of an ensemble of signals that live on a smooth manifold from their under sampled measurements. Unlike current methods that are designed to recover a single signal assuming perfect knowledge of the manifold model, the proposed algorithms exploit similarity between the signals without prior knowledge of the underlying manifold structure. Our first algorithm is a two-step scheme, where the Laplacian of the graph associated with the manifold is estimated from similar under sampled measurements made on the signals; this Laplacian is used to formulate the problem as a penalized optimization scheme, where smoothness of the signals on the manifold is chosen as the penalty. The second algorithm is an iterative scheme that alternates between computation of the Laplacian and the signals. Validation of the proposed algorithms using simulations and experimental MRI data demonstrate their utility in accelerating free breathing cardiac MRI.

Low rank recovery with manifold smoothness prior: Theory and application to accelerated dynamic MRI

We introduce a regularized optimization algorithm to jointly recover signals that live on a low dimensional smooth manifold. The regularization penalty is the nuclear norm of the gradients of the signals on the manifold. We use this algorithm to reconstruct free breathing dynamic cardiac CINE MRI data. A novel acquisition scheme was used to facilitate the estimation of the manifold structure and recover high quality images. The results show that the method is an efficient alternative to traditional breath-held CINE exams.

Subspace based low rank & joint sparse matrix recovery

We consider the recovery of a low rank and jointly sparse matrix from under sampled measurements of its columns. This problem is highly relevant in the recovery of dynamic MRI data with high spatio-temporal resolution, where each column of the matrix corresponds to a frame in the image time series; the matrix is highly low-rank since the frames are highly correlated. Similarly the non-zero locations of the matrix in appropriate transform/frame domains (e.g. wavelet, gradient) are roughly the same in different frame. The superset of the support can be safely assumed to be jointly sparse. Unlike the classical multiple measurement vector (MMV) setup that measures all the snapshots using the same matrix, we consider each snapshot to be measured using a different measurement matrix. We show that this approach reduces the total number of measurements, especially when the rank of the matrix is much smaller than than its sparsity. Our experiments in the context of dynamic imaging shows that this approach is very useful in realizing free breathing cardiac MRI.

Convex clustering and recovery of partially observed data

We propose a convex clustering and reconstruction algorithm for data with missing entries. The algorithm uses a similarity measure between every pair of points to cluster and recover the data. The cluster centres can be recovered reliably when the ground-truth similarity matrix is available. Moreover, the similarity matrix can also be reliably estimated from the partially observed data, when the clusters are well-separated and the coherence of the difference between points from different clusters is low. The algorithm performs well using the estimated similarity matrix on a simulated dataset. The method is also successful in reconstructing images from under-sampled Fourier data.

Two step recovery of jointly sparse and low-rank matrices: Theoretical guarantees

We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common measurements of the columns. In the second step, the subspace aware recovery of the matrix is solved using a simple least square algorithm. The results are verified in the context of recovering CINE data from undersampled measurements; we obtain good recovery when the sampling conditions are satisfied.