Compression, restoration, resampling, 'compressive sensing': Fast transforms in digital imaging

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 tools in image compression, image restoration, image resampling and geometrical transformations and can be traced back to the early 1970s. 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 resampling and image reconstruction from sparse samples and up to the 'compressive sensing' approach that has gained popularity in the last few years. The review has a tutorial character and purpose.