## Appendix B: local similarity

Local similarity between vectors and is defined as:

 (26)

where denotes dot product, and come from two least-squares minimization problems:

 (27) (28)

where is a diagonal operator composed of the elements of , is a diagonal operator composed of the elements of . Note that in equations 26-28, , , and denote vectorized 2D matrices. Equations 27 and 28 can be solved using shaping regularization with a local-smoothness constraint:

 (29) (30)

where is a smoothing operator and and are two parameters controlling the physical dimensionality and enabling fast convergence when inversion is implemented iteratively. These two parameters can be chosen as and .

2020-03-27