We present a new method for data interpolation and signal/noise separation of teleseismic wavefields recorded by regional seismic arrays. The method exploits the plane wave nature of direct arrivals and receiver-side arrivals from regional scale structure by decomposing the recorded wavefield into a plane wave basis using the linear radon transform. Casting the radon transform as an inversion p...

SHORT ABSTRACT: Ship wakes are often used as the primary means to detect ships in SAR images since they can extend for kilometers. On radar images, they often take the appearance of bright and/or dark lines hidden in the sea clutter. For this reason, robust and efficient line detection algorithms are needed. Our first results tend to support the classical method relying on the Radon Transform a...

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...