Abstract #3532

Gini reweighted ℓ1 minimization for rapid MRI

Carlos Castillo-Passi^1,2, Claudia Prieto^1,2,3, Gabriel Varela-Mattatall^1,2, Carlos Sing-Long^2,4,5, and Pablo Irarrazaval^1,2,5

¹Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile, ²Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile, ³Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, United Kingdom, ⁴Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, United States, ⁵Institute for Biological and Medical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

Under-sampling acquisition is oftenly used to reduce the scan time. Compressed Sensing allows the reconstruction of these data by solving a convex optimization problem. This is done to exploit the sparsity of the signals using the ℓ1-norm. We propose to use the Gini Index as a sparsity measure. In this work we demonstrate that this index allow to further increase the under-sampling factor. Interestingly this non-linear index can be computed by solving iteratively reweighted ℓ1 problems, without excessive computational load.

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