1. An image processing apparatus, comprising: a storage device configured to store mode specification information associating a job with a mode, wherein the mode specification information indicates which of a page mode and a band mode is to be selected when the job is performed; a data processing device configured to acquire image data and perform a data processing on the image data; an input device configured to detect a first user operation for inputting the job and a second user operation for starting the job; a main controller configured to (1) specify the mode corresponding to the job designated by the first user operation, and (2) cause the data processing device to acquire the image data upon detection of the second user operation and to perform the data processing according to the specified mode; a data storage device configured to store the image data corresponding to one page; a memory configured to store band data obtained by dividing the image data corresponding to one page, wherein the image data is stored in the memory as the band data when the specified mode is the band mode, and wherein the image data is stored in the data storage device when the specified mode is the page mode; the data processing device is further configured to perform the data processing on the band data read from the memory when the specified mode is the band mode, and wherein the data processing device is further configured to perform the data processing on the image data read from the data storage device when the specified mode is the page mode; and a scanner configured to output the band data of the image data and the band data of attribute data corresponding to the image data, wherein the data processing device comprises a data compression/decompression circuit; and when the specified mode is the page mode, the data compression/decompression circuit is configured to read from the memory the band data of the image data and the band data of the attribute data corresponding to the image data, compress the band data of the image data and the band data of the attribute data corresponding to the image data, store the band data of the image data and the band data of the attribute data corresponding to the image data that have been compressed into the data storage device, read the band data of the image data and the band data of the attribute data corresponding to the image data that have been compressed from the data storage device, decompress the band data of the image data and the band data of the attribute data corresponding to the image data that have been compressed, and store into the memory the band data of the image data and the band data of the attribute data corresponding to the image data.