eduzhai > Applied Sciences > Engineering >

Hadamard Wirtinger Flow for Sparse Phase Retrieval

  • Save

... pages left unread,continue reading

Document pages: 22 pages

Abstract: We consider the problem of reconstructing an $n$-dimensional $k$-sparsesignal from a set of noiseless magnitude-only measurements. Formulating theproblem as an unregularized empirical risk minimization task, we study thesample complexity performance of gradient descent with Hadamardparametrization, which we call Hadamard Wirtinger flow (HWF). Providedknowledge of the signal sparsity $k$, we prove that a single step of HWF isable to recover the support from $k(x^* {max})^{-2}$ (modulo logarithmic term)samples, where $x^* {max}$ is the largest component of the signal in magnitude.This support recovery procedure can be used to initialize existingreconstruction methods and yields algorithms with total runtime proportional tothe cost of reading the data and improved sample complexity, which is linear in$k$ when the signal contains at least one large component. We numericallyinvestigate the performance of HWF at convergence and show that, while notrequiring any explicit form of regularization nor knowledge of $k$, HWF adaptsto the signal sparsity and reconstructs sparse signals with fewer measurementsthan existing gradient based methods.

Please select stars to rate!

         

0 comments Sign in to leave a comment.

    Data loading, please wait...
×