IMAGE PROCESSING INCLUDING ENCODING INFORMATION CONCERNING THE MAXIMUM NUMBER OF SIGNIFICANT DIGITS HAVING LARGEST ABSOLUTE VALUE OF COEFFICIENT DATA IN GROUPS

An image processing apparatus includes: a number of significant digits coding unit encoding information concerning the maximum number of significant digits as the number of significant digits of coefficient data having the largest absolute value in each of groups set in units of the predetermined number of plural coefficient data generated from image data; a zero-run coding unit encoding zero-run formed by a group including only coefficient data a value of which is “0”; an absolute value coding unit encoding absolute values of respective coefficient data other than zero-run with respect to each group; and a sign coding unit encoding positive and negative signs of respective coefficient data other than zero-run with respect to each group.