Interpolation and gradient estimation of images using the discrete cosine transform

A signal can be represented completely by the weighted sum of any complete orthonormal set of basis functions. The discrete cosine transform (DCT) has long been used in image processing because, short of the Karhunen-Loeve transform, it typically provides the highest amount of compression of the image transforms commonly used. In addition to its use in compression, the DCT may also be used as a set of basis functions. We demonstrate how the DCT basis functions may be used to interpolate an image and provide a gradient estimate at interpolated points.