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Transform image processing methods are methods that work in domains of image transforms, such as Discrete Fourier, Discrete Cosine, Wavelet, and alike. They proved to be very efficient in image compression, in image restoration, in image resampling, and  in geometrical transformations and can be traced back to early 1970s. The paper reviews these methods, with emphasis on their comparison and relationships, from the very first steps of transform image compression methods to adaptive and local adaptive filters for image restoration and up to “compressive sensing” methods that gained popularity in last few years. References are made to both first publications of the corresponding results and more recent and more easily available ones. The review has a tutorial character and purpose

Fast Transforms in Image Processing: Compression, Restoration, and Resampling