Compression, Restoration, Re-sampling, Compressive Sensing: Fast Transforms in Digital Imaging
This is an incremental tutorial review for researchers in digital imaging, summarizing existing methods without introducing novel contributions.
The paper reviews transform image processing methods, covering their evolution from early compression techniques to modern applications like compressive sensing, without presenting new experimental results.
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.