Välkommen till en föreläsning i seminarieserien i matematik.
A common technique for solving ill-posed inverse problems is to include some sparsity constraint, and pose it as a convex optimization problem, as is done e.g. in compressive sensing. The corresponding functional to be minimized often includes an l2 data fidelity term plus a convex term forcing sparsity. However, for many applications a non-convex term would be more suitable, although this is discarded since it leads to issues with algorithm convergence, local minima etc. I will introduce a new transform to convexify non-convex functionals of the above type. Applications include low rank approximation, multi-dimensional frequency estimation, phase retrieval, GPS-positioning, among others. I will discuss some of these if time allows.
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