1. An image processing apparatus comprising: a filtering process circuit that performs an image filtering process that includes a plurality of times of filtering processes with respect to original image data to acquire processed image data; a gain candidate data storage; and a gain specifying circuit; wherein in each of the plurality of times of filtering processes, the filtering process circuit applies a filter to processing target data to acquire filter application process data, applies a gain to the filter application process data to acquire gain application process data, and acquires filtering process data from the gain application process data, wherein in each of the plurality of times of filtering processes, the gain applied to the filter application process data is acquired based on a target frequency characteristic of the image filtering process specified based on an individual optical characteristic of an optical system used when the original image data is acquired, the gain candidate data storage stores gain table information obtained by associating candidate data of the gain applied to the filter application process data with the individual optical characteristic of the optical system, in each of the plurality of times of filtering processes, and the gain specifying circuit specifies, with reference to the gain table information, the candidate data associated with the individual optical characteristic of the optical system used when the original image data is acquired as the gain applied to the filter application process data in each of the plurality of times of filtering processes, wherein the filtering process circuit applies the gain specified by the gain specifying circuit to the filter application process data to acquire the gain application process data in each of the plurality of times of filtering processes.