  Transform image processing methods are methods that work in domains of image
transforms, such as Discrete Fourier, Discrete Cosine, Wavelet and alike. They
are the basic tool in image compression, in image restoration, in image
re-sampling and geometrical transformations and can be traced back to early
1970-ths. The paper presents a review of these methods with emphasis on their
comparison and relationships, from the very first steps of transform image
compression methods to adaptive and local adaptive transform domain filters for
image restoration, to methods of precise image re-sampling and image
reconstruction from sparse samples and up to "compressive sensing" approach
that has gained popularity in last few years. The review has a tutorial
character and purpose.
