An image encoder and a method thereof using a coordinate conversion of differential image for decoding the image are provided to encode input image efficiently by performing a DCT(Discrete Cosine Transform) by using a basis vector. An input image divider(510) divides an input image into a plurality of image blocks including a conversion object block. A pixel coordinates converter(550) converts the coordinate of a first pixel included in the conversion object block into the coordinates of the second pixel within the conversion object block. A coding unit encodes the conversion object block transformed of coordinate. The pixel coordinate conversion unit converts the coordinates of the first pixel in consideration of the direction of the base vector of the discrete cosine transform.
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