I am a PhD student working on inverting gravity data for depth estimation. I have applied the Gaussian Least Squares method to solve the linearized inverse problem for 3D density estimation and obtained very stable results. However, for depth estimation, the Gaussian Least Squares approach remains stable only in the vicinity of the initial model, particularly when 50% Gaussian noise is added to the exact model and the data is noise-free.

I have also tested the Conjugate Gradient Least Squares method, but it performed worse than the Gaussian Least Squares in this context. I am not considering global optimization techniques, as they are highly time-consuming, especially with a large number of model parameters.

I would like to inquire if there are other methods for solving the linearized inverse problem that can provide more stable depth estimations.

Thank you in advance.