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Transform image processing methods are methods that work in domains of imagetransforms, such as Discrete Fourier, Discrete Cosine, Wavelet and alike. Theyare the basic tool in image compression, in image restoration, in imagere-sampling and geometrical transformations and can be traced back to early1970-ths. The paper presents a review of these methods with emphasis on theircomparison and relationships, from the very first steps of transform imagecompression methods to adaptive and local adaptive transform domain filters forimage restoration, to methods of precise image re-sampling and imagereconstruction from sparse samples and up to "compressive sensing" approachthat has gained popularity in last few years. The review has a tutorialcharacter and purpose.

Compression, Restoration, Re-sampling, Compressive Sensing: Fast Transforms in Digital Imaging