2 research outputs found
Regularized Linear Inversion with Randomized Singular Value Decomposition
In this work, we develop efficient solvers for linear inverse problems based
on randomized singular value decomposition (RSVD). This is achieved by
combining RSVD with classical regularization methods, e.g., truncated singular
value decomposition, Tikhonov regularization, and general Tikhonov
regularization with a smoothness penalty. One distinct feature of the proposed
approach is that it explicitly preserves the structure of the regularized
solution in the sense that it always lies in the range of a certain adjoint
operator. We provide error estimates between the approximation and the exact
solution under canonical source condition, and interpret the approach in the
lens of convex duality. Extensive numerical experiments are provided to
illustrate the efficiency and accuracy of the approach.Comment: 20 pages, 4 figure