Data in multidimensional space such as a two-dimensional image is encoded with high efficiency. Further, as two-dimensional data can be decomposed to one-dimensional bases, the problem of wiring for two-dimensional parallelizing in a convolution arithmetic unit can be solved. For this purpose, two-dimensional image data f(x,y) to be encoded is inputted, and one-dimensional adaptive bases X(x),Y(y) representing the two-dimensional image are obtained. Next, a reconstructed image is generated based on the one-dimensional adaptive bases, and the one-dimensional adaptive bases are corrected based on an error E between the reconstructed image and the input image. The correction is repeated until the error E is reduced.