High order l1 regularization techniques for reconstructing images from Fourier data

Anne Gelb

Mathematics, Dartmouth College.

In this talk we investigate accurate and efficient l1 regularization methods for generating images from Fourier data. As a prototype, we will consider synthetic aperture radar (SAR).

Although l1 regularization algorithms are already employed in many imaging applications, in particular magnetic resonance imaging (MRI), tomographic imaging, and SAR, practical and efficient implementation in terms of real time imaging often remain a challenge.

Here we demonstrate that fast numerical operators can be used to robustly implement high order l1 regularization methods that are as or more efficient than traditional approaches such as back projection, while providing superior image quality. We also develop a sequential joint sparsity model which naturally combines the joint sparsity methodology with composite imaging methods. Our technique is able to reduce the effects of speckle and other noisy artifacts with little additional computational cost. Finally we show that generalizing total variation regularization to non-integer and higher orders provides improved flexibility and robustness.

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