|Adaptive multiple subtraction using regularized nonstationary regression|
I have presented a general method for regularized nonstationary regression. The key idea is the application of shaping regularization for constraining the variability of nonstationary coefficients. Shaping regularization has clear advantages over conventional Tikhonov's regularization: a more intuitive selection of regularization parameters and a faster iterative convergence because of better conditioning and eigenvalue clustering of the inverted matrix.
I have shown examples of applying regularized regression to benchmark tests of adaptive multiple subtraction. When the signal characteristics change with time or space, regularized nonstationary regression provides an effective description of the signal. This approach does not require breaking the input data into local windows, although it is analogous conceptually to sliding (maximum overlap) spatial-temporal windows.