Ray's lasso fusion upgrade makes Occam inversion sharper and faster

Anandaroop Ray's latest arXiv paper (2608.14225) modernizes Occam's inversion, a classic geophysical algorithm that finds the smoothest model consistent with observations. Traditionally, Occam's inversion penalizes l2 model roughness, which prevents overinterpretation but blurs sharp boundaries. Ray introduces l1 regularization—specifically lasso fusion and total variation—to produce visually sharp, edge-preserving models. He rigorously shows that for l2 data norms and l1 model penalties, the synthesis and analysis formulations of lasso fusion collapse to the same 1D problem, and he clarifies the often-overlooked distinction between isotropic and anisotropic total variation in multiple dimensions. The framework also extends to overcomplete dictionaries, including wavelet transforms, bridging geophysics with modern statistical and imaging literature.

Ray benchmarks three solvers—coordinate descent, iteratively reweighted least squares (IRLS), and split Bregman—across linear problems (1D regression, 2D deblurring) and a nonlinear case (1D airborne transient electromagnetics) using field data. His results are actionable: coordinate descent is recommended for 1D problems, while IRLS wins for 2D, requiring up to an order of magnitude fewer least squares solves than split Bregman. These findings lower the barrier for geophysicists to adopt l1 regularized inversion, potentially improving subsurface imaging, resource exploration, and environmental monitoring—all through a familiar Occam-style lens.