Stability estimates for the local Radon transform. (12th February 2018) - Andersson, Joel; Boman, Jan
Abstract: We consider the inverse problem for the 2-dimensional local Radon transform R [  f  ], where f is supported in y ⩾ x 2 and R [ f ] ( ξ, η ) = ∫ f ( x, ξ x + η ) d x is defined near ( ξ, η ) = ( 0, 0 ) . We give logarithmic estimates of f in terms of R [  f  ] for functions f that satisfy an a priori bound. For a certain class of smooth, positive weight functions m we give similar estimates for the weighted Radon transform R m | f ] ( ξ, η ) = ∫ f ( x, ξ x + η ) m ( ξ, η, x ) d x .