In order to provide an X-ray CT apparatus and the like that reconstruct an image using an iterative approximation method which ensures stable convergence and can be executed at high speed, a computation device 5 of an X-ray CT apparatus 1 calculates matrices A, B, D, R, and R′ on the basis of the scanning conditions input through an input device 6 (step 1). Then, the computation device 5 calculates each element of a matrix I−α(SBTDA+βSR) (step 2). Then, the computation device 5 calculates the operator norm ∥I−α(SBTDA+βSR)∥ of the matrix I−α(SBTDA+βSR) (step 3). Then, the computation device 5 determines a relaxation coefficient α such that a predetermined conditional expression is satisfied (step 4).
