Nonlinear Approximation of Images with Haar-Like Four-Point Orthogonal Transforms

We study simple linear orthogonal transforms for images, which are real-valued, non-overlapped, and fast transforms similar to the Haar wavelet transform. These transforms reveal the correlation of each block of four neighbor points (or pixels) of an image, and can thus be used for an efficient representation of the image. Since several parameters are necessary to determine the orthogonality of such transforms, we conducted numerical experiments to determine the optimal parameter for minimizing distortion errors in nonlinear image approximations.