The relation between Radon transform and orthogonal expansions of a function on the unit ball in R is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to algorithms for image reconstruction from Radon data. The relation between orthogonal expansion and the singular value decomposition of the Radon transform is also exploited.

The fused floating point add-subtract unit is useful for digital signal processing (DSP) applications Such as fast Fourier transform (FFT) & discrete cosine transform (DCT) butterfly operations. To improve the performance of fused floating point addsubtract unit, a dual path algorithm& pipelining algorithms are useful .The designs are implemented for both single and double precision. The fused ...

We discuss Hough Transform, some of its key properties, a scheme of fast and complete calculation of the Hough Transform (similar to the Fast Fourier Transform), and an efficient implementation of this scheme on SIMD processors. We also demonstrate an application of the Fast Hough Transform in computer vision by the example of an automatic page orientation detection unit incorporated in an inte...

Many signals can be described as functions on the unit disk (ball). In the framework of group representations it is well-known how to construct Hilbert-spaces containing these functions that have the groups SU(1,N) as their symmetry groups. One illustration of this construction is three-dimensional color spaces in which chroma properties are described by points on the unit disk. A combination o...

X-ray free electron lasers are used in measuring diffraction patterns from nanocrystals in the 'diffract-before-destroy' mode by outrunning radiation damage. The finite-sized nanocrystals provide an opportunity to recover intensity between Bragg spots by removing the modulating function that depends on crystal shape, i.e. the transform of the crystal shape. This shape-transform dividing-out sch...

In this paper, the k-trigonometric functions over the Galois Field GF(q) are introduced and their main properties derived. This leads to the definition of the cask(.) function over GF(q), which in turn leads to a finite field Hartley Transform . The main properties of this new discrete transform are presented and areas for possible applications are mentioned.