An image encoding apparatus reduces the discontinuation or elimination of thin lines during a transform process including rounding of coefficient data generated by a frequency transform, thereby enabling the ready acquisition of a high-quality reduced image. The image encoding apparatus includes a frequency transform unit configured to frequency-transform an image to generate coefficient data having a low-frequency component and a high-frequency component; a dynamic range control unit configured to add a bit on a least significant bit end of a portion of pixel data of the image that is used for generating the coefficient data of the low-frequency component on a pixel by pixel basis, thereby increasing a dynamic range of the pixel data; and an encoding unit configured to encode the coefficient data generated by the frequency transform unit.