This paper extends the concepts of the Sparse Fast Fourier Transform (sFFT) Algorithm introduced in [1] to work with two dimensional (2D) data. The 2D algorithm requires several generalizations to multiple key concepts of the 1D sparse Fourier transform algorithm. Furthermore, several parameters needed in the algorithm are optimized for the reconstruction of sparse image spectra. This paper add...

The generalized Fourier transform associated with a selfadjoint Sturm–Liouville operator is a unitary transformation which converts the action of this operator into a simple product by a spectral variable. For a particular operator defined on the half-line and which involves a step function, we show how to extend such a transformation to generalized functions, or distributions, with a suitable ...

In this paper, a novel two-dimensional Discrete Fourier Transform based information embedding has been proposed for color image authentication (2D-DFTSDECIA). Initially, each 2 × 2 sub-image block of the carrier image is pre-adjusted, if necessary and then transformed by the application of two dimensional Discrete Fourier Transforms (2D-DFT) where the transformation technique has been applied i...

Introduction Magnetic resonance cholangiopancreatography (MRCP) is evolving as an effective non-invasive imaging technique for examining patients with suspected pancreatic or biliary disease. The two dimensional (2D) half-Fourier RARE sequence is one of optimal pulse sequences for the standard MRCP (1). However the 2D halfFourier RARE sequence have several limitations such as lower spatial reso...

As a generalization of the 2D Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics and signal and image processing. To reduce the digital implementation complexity of the 2D NsLCT, some previous works decomposed the 2D NsLCT into several low-complexity operations, including 2D FT, 2D chirp multiplication (2D...

We present an open-source ITK implementation of a direct Fourier method for tomographic reconstruction, applicable to parallel-beam x-ray images. Direct Fourier reconstruction makes use of the central-slice theorem to build a polar 2D Fourier space from the 1D transformed projections of the scanned object, that is resampled into a Cartesian grid. Inverse 2D Fourier transform eventually yields t...

the analysis of geochemical data in frequency domain, as indicated in this research study, can provide new exploratory informationthat may not be exposed in spatial domain. to identify deep geochemical anomalies, sulfide zone and geochemical noises in dalli cu–au porphyry deposit, a new approach based on coupling fourier transform (ft) and principal component analysis (pca) has beenused. the re...

Wavelet transformation is one of the most practical mathematical transformations in the field of image processing, especially image and signal processing. Depending on the nature of the multiresolution analysis, Wavelet transformation become more accessible and powerful tools. In this paper, we refer to the mathematical foundations of this transformation.   Introduction: The...