A method including: generating an updated subsurface property model of a subsurface region, with a computer, from an initial estimate of the subsurface property model by performing an iterative inversion, which includes inverting geophysical data to infer the updated subsurface property model, wherein the generating the updated subsurface property model includes linearly remapping the initial estimate of the subsurface property model based on an inverse of a regularization operator, included with the initial estimate of the subsurface property model, into one in which the regularization operator is represented by an identity matrix, performing a unitary matrix decomposition in order to group the identity matrix with sparse matrices output from the unitary matrix decomposition, and performing a search over at least one trade-off parameter to reduce a misfit between simulated data generated from a most recent estimate of the subsurface property model and the geophysical data until a predetermined stopping criteria is satisfied; and generating, with a computer, an image of the subsurface region using the updated subsurface property model.