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

TL;DR

This paper reviews various transform-based image processing techniques, including compression, restoration, re-sampling, and compressive sensing, highlighting their evolution, relationships, and recent advances in the field.

Contribution

It provides a comprehensive tutorial review of transform methods in digital imaging, covering historical developments and recent adaptive and compressive sensing approaches.

Findings

Comparison of transform methods in image processing

Discussion of adaptive and local adaptive filters

Overview of recent compressive sensing techniques

Abstract

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.