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This work is concerned with the structure of bilinear minimization problems arising in recovering sub-sampled and modulated images in parallel magnetic resonance imaging. By considering a physically reasonable simplified model exhibiting the same fundamental mathematical difficulties, it is shown that such problems suffer from poor gradient scaling and… (More)

The Cartesian parallel magnetic imaging problem is formulated variationally using a high-order penalty for coil sensitivities and a total variation like penalty for the reconstructed image. Then the optimality system is derived and numerically discretized. The objective function used is non-convex, but it possesses a bilinear structure that allows the… (More)

We present a fast and efficient spectral method for computing the eigenvalues and eigenfunctions for a one-dimensional piecewise smooth potential, as arises in the case of epitaxially grown semiconductor heterostructures. Many physical devices such as quantum well infrared photodetectors and quantum cascade lasers rely upon transitions between bound and… (More)

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