Leonid Yaroslavsky

Leonid Yaroslavsky

A problem is addressed of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy. A sampling theory based method of image sampling and reconstruction is suggested that allows to draw near the minimal rate of image sampling defined by the sampling theory. Presented and discussed are also results of experimental verification of the method and its possible applicability extensions.

Leonid Yaroslavsky

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.