Tensor Decompositions and Applications
SIAM Review
Matrix completion from a few entries
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Low rank matrix recovery for real-time cardiac MRI
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Fixed point and Bregman iterative methods for matrix rank minimization
Mathematical Programming: Series A and B
Low rank matrix recovery for real-time cardiac MRI
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
ADMiRA: atomic decomposition for minimum rank approximation
IEEE Transactions on Information Theory
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There has been significant recent interest in fast imaging with sparse sampling. Conventional imaging methods are based on Shannon-Nyquist sampling theory. As such, the number of required samples often increases exponentially with the dimensionality of the image, which limits achievable resolution in high-dimensional scenarios. The partially-separable function (PSF) model has previously been proposed to enable sparse data sampling in this context. Existing methods to leverage PSF structure utilize tailored data sampling strategies, which enable a specialized two-step reconstruction procedure. This work formulates the PSF reconstruction problem using the matrix-recovery framework. The explicit matrix formulation provides new opportunities for data acquisition and image reconstruction with rank constraints. Theoretical results from the emerging field of low-rank matrix recovery (which generalizes theory from sparse-vector recovery) and our empirical results illustrate the potential of this new approach.