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The high resolution image restoration method from a down-sampled low resolution image by using the discrete cosine transform (DCT) is proposed. The downsampling process is modeled in matrix form and the similar transformation by the DCT matrix makes the downsampling matrix to be a sparse matrix. Then the restored high resolution image can be expressed in a scalar form by using the similar transformation and efficiently computed from the low resolution image. Computer simulations show that the proposed method is superior to the cubic spline interpolation in the high resolution image restoration performance.