1. An image sensor comprising: an image generating unit configured to generate a pixel image corresponding to intensity of incident light; and a bad pixel processing circuit configured to detect a bad pixel, and to output a compensated pixel image, wherein the bad pixel processing circuit comprises: a bad pixel detection unit configured to determine whether a representative pixel representing at least one bad pixel is included in a kernel, the kernel having a first pixel at a center of the kernel, and to determine whether the first pixel is a bad pixel when the representative pixel is included in the kernel; and a bad pixel compensation unit configured to compensate for the first pixel using a second pixel in the kernel when the first pixel is determined to be a bad pixel, and to output the compensated pixel image, wherein first data including only coordinates of the representative pixel are stored as representative pixel information in a bad pixel memory and the bad pixel detection unit determines whether the first pixel is a bad pixel using the coordinates.