due to some difficulties during seismic data acquisition, like natural obstacles (high voltage electricity cable, bad coupling of geophones with the ground) some of the traces cannot be recorded. since bad traces make the final stack unclear, usually bad traces go mute while processing. the final image of the earth’s crust is highly dependent of the quality and resolution of acquired data and m...

In this paper we define a discrete analogue of the continuous diffracted projection. we define a discrete diffracted transform (DDT) as a collection of the discrete diffracted projections taken at specific set of angles along specific set of lines. We define ‘discrete diffracted projection’ to be a discrete transform that is similar in its properties to the continuous diffracted projection. We ...

The Radon transform (1) is a key mathematical tool in tomography. Its inverse enables one to reconstruct a function if some of its integrals are known. The whole subject has been recently revived by quantum mechanical applications. The possibility of reconstructing the tomographic map of the Wigner quasidistribution function (2, 3, 4) associated with a given quantum state (5, 6, 7) has motivate...

The Radon transform on a group A is a linear operator on the space of functions /: A-+ C. It is shown that if A = Z;: then the Radon transform with respect to a subset B c .4 is not invertible if and only if B has the same number of elements in every coset of some maximal subgroup of A. The same does not hold in general for arbitrary finite abelian groups. ' IW7 ACxhlK I%\\. 1°C Let A be a fini...

The Hua-Radon and polarized transform are two orthogonal projections defined on holomorphic functions in the Lie sphere. Both transformations can be written as integral transforms with respect to a suitable reproducing kernel. Integrating both kernels over Stiefel manifold yields linear combination of zonal spherical monogenics. Using an Almansi type decomposition properties monogenics, we obta...

Because the Radon transform is a smoothing transform, any noise in the Radon data becomes magnified when the inverse Radon transform is applied. Among the methods used to deal with this problem is the wavelet-vaguelette decomposition (WVD) coupled with wavelet shrinkage, as introduced by Donoho (1995). We extend several results of Donoho and others here. First, we introduce a new sufficient con...

Brachiopods have a lateral outline which is quite important in systematic studies. It is often assessed by a qualitative evaluation and linear measurements, which are not clear enough and precise for describing the shape of the shell and its changes In this paper we propose a new method for classification of fossils based on the radon transform from their greyscale image. We take the case of br...

Finite Radon Transform mapper has the ability to increase orthogonality of sub-carriers, it is non sensitive to channel parameters variations, and has a small constellation energy compared with conventional Fast Fourier Transform based orthogonal frequency division multiplexing. It is also able to work as a good interleaver which significantly reduces the bit error rate. Due to its good orthogo...