Image restoration from a downsampled image by using the DCT

The high-resolution (HR) image restoration from a downsampled low-resolution (LR) image by using the discrete cosine transform (DCT) is proposed. The downsampling process is modeled in matrix form and the DCT is applied to the downsampling matrix to obtain the sparse matrix representation. The restored HR image is then efficiently computed from the LR image by using the sparsity. The distortion caused by the observation noise is theoretically analyzed, and the power of distortion is shown to be closely equal to the variance of the observation noise. Computer simulations show that the proposed method is superior to the cubic spline interpolation in the HR image restoration performance as far as the amount of the additive noise is small.