Least-squares diffraction imaging using shaping regularization by anisotropic smoothing |

For inversion we adopt a conjugate gradients scheme (Fomel et al., 2007):

where and are anisotropic-smoothing and thresholding operators, is the gradient at iteration , is a conjugate direction, is an update step length , and is designed to guarantee that and are conjugate. After several internal iterations of the conjugate gradient algorithm we generate , to which we apply thresholding to drop samples corresponding to noise with values lower than the threshold , and which we then smooth along edges by applying anisotropic smoothing operator . Outer model shaping iterations are denoted by .

Inversion results also depend on the numbers of inner and outer iterations: their tradeoff determines how often shaping regularization is applied and therefore controls its strength. Regularization by early stopping can also be conducted. The optimization strategy with removed corresponds to the iterative thresholding approach (Daubechies et al., 2004).

Least-squares diffraction imaging using shaping regularization by anisotropic smoothing |

2021-02-24