1. An image reading apparatus, comprising: a reading unit that reads an image of an original at a reading position while conveying the original, a detection unit that, based on image data obtained by reading a white image at the reading position with the reading unit, detects an abnormal pixel based on a foreign substance adhering to the reading position and outputs data indicating a position of the abnormal pixel, a correction unit that, based on the data outputted from the detection unit, corrects image data obtained by reading an original at the reading position with the reading unit, a timer that times a time period required to detect the abnormal pixel, a first control unit that, in a case where a plurality of originals are continuously conveyed and read with the reading unit and a time period that has been timed by the timer is less than a predetermined time period, performs control so that detection of the abnormal pixel by the detection unit is carried out prior to reading of a first original of the plurality of originals, and a correction process by the correction unit based on the data indicating the position of the abnormal pixel is carried out on image data obtained by reading the first original, and a second control unit that, in a case where a plurality of originals are continuously conveyed and read with the reading unit and the time period that has been timed by the timer is equal to or greater than the predetermined time period, performs control so that detection of the abnormal pixel by the detection unit is carried out prior to reading of a first original of the plurality of originals, and the correction process by the correction unit based on the data indicating the position of the abnormal pixel is carried out on image data obtained by reading a second original following the first original.