Images are typically described via orthogonal, non-redundant transforms like wavelet or discrete cosine transform. The good performances of wavelets in one-dimensional domain are lost when they are applied to images using 2D separable basis since they are not able to efficiently code one-dimensional singularities. The Ridgelet transform achieves very compact representation of linear singulariti...

Citation Zhang, Haijiang et al. " Three-dimensional passive seismic waveform imaging around the SAFOD site, California, using the generalized Radon transform. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how th...

This article deals with the problem of the determination of characteristics of imperfect circular objects in discrete images, namely the radius and center coordinates. To limit distortion, a multilevel method based on active contours was developed. Its originality is to furnish a set of geometric envelopes in one pass, with a correspondence between grayscale and a regularity scale. The adequacy...

Wireless digital communication networks are rapidly expanding resulting in a demand for reliable and high spectral efficiency systems. Multi-Carrier Code Division Multiple Access (MC-CDMA) has emerged recently as a promising candidate for the next generation broad-band mobile networks. Also it was found recently that Radon-discrete wavelet transform (DWT) based Orthogonal Frequency Division Mul...

Objective: To acknowledge the work and life of the Austrian mathematician Johann Radon, motivated by a historical narrative on the development of the computed tomography scanner. Methods: Information was obtained from journal articles, textbooks, the Nobel web site, and proceedings from mathematical symposiums. Results: The computed tomography scanner changed the paradigm of medical imaging. Th...

In this paper, we address the problem of the rotationinvariant texture analysis. For this purpose, we first present a modified version of the discrete Radon transform whose performance, including accuracy and processing time, is significantly better than the conventional transform in direction estimation and categorization of textural images. We then utilize this transform with a rotated versio...

This paper outlines methods to perform basic spatial operations on 2D digital images that have been mapped into an equivalent set of digital projections. The digital projections are generated using the Discrete Radon Transform (DRT). Each digital projection is similar to an oriented straight-line integral of the Radon transform and the set of digital projections resembles the sinogram from clas...

In this paper, we present some new relationship between the divergent beam projection and the Radon transform. An application of our results is to implement the Radon inversion from divergent beam projection.

We develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross section of a body, using almost completely local data that significantly reduces the amount of exposure and computations in X-ray tomography. The p...

Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle ω = Sθ in terms of the incoming angle with S orthogonal and Id−S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact...