1. An imaging device comprising: a taking lens having a plurality of regions, the plurality of regions each with an independent characteristic; an image pickup element having a plurality of light-receiving sensors provided so as to correspond to the plurality of regions, the plurality of light-receiving sensors performing pupil division of a light beam passing through any of the plurality of regions for selective light-receiving; an image generating unit which generates, from an imaging signal from a light-receiving sensor corresponding to one region of the plurality of regions, an image corresponding to the one region; and an image correcting unit which corrects the generated image, wherein, the independent characteristic is at least either one of a focal length and a focal distance, and the image correcting unit performs removal of an influence of a light beam passing through a region other than the one region from the image generated so as to correspond to the one region based on the following equation: 
 ( A 1 , A 2 ,. .. , A N ) T =X −1 ·( A 1 ′, A 2 ′,. .. , A N ′) T , where N: a number of the regions of the taking lens (an integer equal to two or more), A i (x, y): an imaging signal after correction of the influence of the light beam passing through another region corresponding to the region i (i=1 to N), A i ′(x, y): an imaging signal before correction of the influence of the light beam passing through another region corresponding to the region i (i=1 to N), X −1 an inverse matrix of a matrix X formed of main gain and crosstalk components, where X ii =S i (x, y) (main gain of the region i; i=1 to N), and X ji =C ji (x, y) (crosstalk component from the region j to the region i; j=1 to N, j ≠ i), and (x, y): picture element position of an image corresponding to a region i.