Compression, restoration, resampling, ‘compressive sensing’: fast transforms in digital imaging

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 resampling 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 resampling 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.

Modeling the Flux of Volatile Fatty Acid in Membrane Distillation with the Effect of Ph

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Digital signal processing in telecommunications based on parametric discrete Fourier transform

“…Let us prove that the linearity, shift, correlation, and Parseval theorems are valid for DFT-P. We introduce the symbolic notation for DFT-P and DDPF-P, defined respectively by relations (4) and 7, as well as for ) (n x  relation (8):…”

“…The methods of vector 1 and spectral 2 digital signal processing (DSP) play a crucial role in information technologies, which are currently widely used in telecommunications [1][2][3][4][5][6]. The relevance of the digitalization of telecommunications is mainly due to two reasons.…”

Sliding signal processing in telecommunication networks based on two-dimensional discrete Fourier transform

“…The classical method of spatial-frequency processing of two-dimensional discrete signals is the 1-D and 2-D discrete Fourier transform (DFT), which allows to obtain a 1-D and 2-D frequency spectrum [1][2][3][4][5][6][7][8][9][10][11][12][13]. At the same time, there are a number of applications [9][10][11][12] where it is necessary to find the values of the frequency spectrum not at all 1-D and 2-D frequencies, but at a subset of them.…”