1. An image reconstruction apparatus comprising: a transmission signal generation unit configured to generate a transmission signal in an image reconstruction region, in order to acquire an image reconstruction value; an electromagnetic wave measurement unit configured to measure electromagnetic waves by receiving the transmission signal; an image reconstruction unit configured to update a parameter by using a matrix of matched system of a Sinc-Gauss-shaped basis function which is allocated to each node of a reconstruction mesh in the image reconstruction region, and generate an image reconstruction value; and an optimization determination unit configured to determine whether the parameter of the image reconstruction unit is optimized or not, and output the image reconstruction value or cause the image reconstruction unit to repetitively perform the calculation, wherein the reconstruction mesh has a grid structure of which the size is larger than that of a forward mesh and equal to the image spatial resolution.