Radon transforms of the Wigner operator on hyperplanes

The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution-a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.

L^p Estimates for Singular Radon Transforms with Rough Kernels

The purpose of this paper is to study the mapping properties of the singular Radon transforms with rough kernels. Such singular integral operators are proved to be bounded on Lebesgue spaces.

High-resolution frequency-domain Radon transform and variable-depth streamer data deghosting

Receiver ghost reflections adversely affect variable-depth streamer （VDS） data acquisition. In addition, the frequency notches caused by the interference between receiver ghosts and primary waves strongly affect seismic data processing and imaging. We developed a high-resolution Radon transform algorithm and used it to predict receiver ghosts from VDS data. The receiver ghost reflections are subtracted and removed from the raw data. We propose a forward Radon transform operator of VDS data in the frequency domain and, based on the ray paths of the receiver ghosts, we propose an inverse Radon transform operator. We apply the proposed methodology to model and field data with good results. We use matching and subtracting modules of commercially available seismic data processing software to remove the receiver ghosts. The frequency notches are compensated and the effective frequency bandwidth of the seismic data broadens.

Multiple attenuation using λ–f domain high-resolution Radon transform

The parabolic Radon transform has been widely used in multiple attenuation. To further improve the accuracy and efficiency of the Radon transform, we developed the 2- fdomain high-resolution Radon transform based on the fast and modified parabolic Radon transform presented by Abbad. The introduction of a new variable 2 makes the transform operator frequency-independent. Thus, we need to calculate the transform operator and its inverse operator only once, which greatly improves the computational efficiency. Besides, because the primaries and multiples are distributed on straight lines with different slopes in the 2-fdomain, we can easily choose the filtering operator to suppress the multiples. At the same time, the proposed method offers the advantage of high-resolution Radon transform, which can greatly improve the precision of attenuating the multiples. Numerical experiments suggest that the multiples are well suppressed and the amplitude versus offset characteristics of the primaries are well maintained. Real data processing results further verify the effectiveness and feasibility of the method.

GEOMETRICALLY INVARIANT WATERMARKING BASED ON RADON TRANSFORMATION

The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new image- watermarking method is presented to resist Rotation, Scale and Translation (RST) attacks. The watermark is embedded into a domain obtained by taking Radon transform of a circular area selected from the original image, and then extracting Two-Dimensional (2-D) Fourier magnitude of the Radon transformed image. Furthermore, to prevent the watermarked image from degrading due to inverse Radon transform, watermark signal is inversely Radon transformed individually. Experimental results demonstrate that the proposed scheme is able to withstand a variety of attacks including common geometric attacks.

Auto detection of wood texture orientation by Radon transform

A novel and efficient approach for detecting wood texture orientation by computer was presented. Four Matlab functions were tried to describe the relative position and orientation of wood texture pixels, to detect texture shape and to create skeletal lines image of wood texture, and BWMORPH function was found the best one. Then by Radon transform, it generated a signature composed of 180 values, each value summing up the size of texture lines that are shaped along that angle, and a two dimensional curve plot was drawn to represent the texture orientation of wood. Furthermore, it analyzed texture orientations of forty species as well as their general statistic laws, classified by softwood, hardwood, radial section and tangential section, and the results showed that texture orientation laws described by Radon trans- form plot and their extracting datum were in accord with the impression of wood texture that people possessed in daily life, which con- firmed the validity of this new approach and their appealing utilization potentials.

RECONSTRUCTION OF THE ATTENUATED RADON TRANSFORM IN π-SCHEME SHORT-SCAN SPECT

In this work, the image reconstruction in π-scheme short-scan single-photon emission computed tomography （SPECT） with nonuniform attenuation is derived in its most general form when π-scheme short-scan SPECT entails data acquisition over disjoint angular intervals without conjugate views totaling to π radians. The reconstruction results are based on decomposition of Novikov＇s inversion operator into three parts bounded in the L2 sense. The first part involves the measured partial data; the second part is a skew-symmetric operator; the third part is a symmetric and compact contribution. It is showed firstly that the operators involved belong to L（L^2（B）. Furthermore numerical simulations are conducted to demonstrate the effectiveness of the developed method.

A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R^n

The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.

Diffraction separation and imaging based on double sparse transforms

Reflection imaging results generally reveal large-scale continuous geological information,and it is difficult to identify small-scale geological bodies such as breakpoints,pinch points,small fault blocks,caves,and fractures,etc.Diffraction imaging is an important method to identify small-scale geological bodies and it has higher resolution than reflection imaging.In the common-offset domain,reflections are mostly expressed as smooth linear events,whereas diffractions are characterized by hyperbolic events.This paper proposes a diffraction extraction method based on double sparse transforms.The linear events can be sparsely expressed by the high-resolution linear Radon transform,and the curved events can be sparsely expressed by the Curvelet transform.A sparse inversion model is built and the alternating direction method is used to solve the inversion model.Simulation data and field data experimental results proved that the diffractions extraction method based on double sparse transforms can effectively improve the imaging quality of faults and other small-scale geological bodies.

The Harmonic Decomposition Reconstruction for the Exponential Radon Transform

The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.

DETECTION OF SHIP WAKES IN SAR IMAGE USING ROTATED WINDOW RADON TRANSFORM

A novel method of rotated window Radon transform is developed for identifying the linear texture in SAR image.It is applied to automatic detection of the ship wakes of SEASAT SAR image.The location and direction of the traveling ship can be quickly and accurately detectec,In some cases, the ship velocity can also be obtained.

Fractional Radon Transform and Transform of Wigner Operator

Based on the Radon transform and fractional Fourier transform we introduce the fractional Radon trans-formation (FRT). We identify the transform kernel for FRT. The FRT of Wigner operator is derived, which naturallyreduces to the projector of eigenvector of the rotated quadrature in the usual Radon transform case.

Relation between Fresnel transform of input light field and the two-parameter Radon transform of Wigner function of the field

This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.

Cone-beam local reconstruction based on a Radon inversion transformation

The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-backprojection （FBP） algorithm based on the Radon inversion transform is presented to deal with the three-dimensional （3D） local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography （ATRACT）, not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.

The Numerical Method of Inversion for the Interior Radon Transform

The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction of a singular value decomposition for R. This immediately leads to an inversion formula by series expansion and range characterizations.

CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM

The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.

GENERALIZED WAVELETS AND INVERSION OF THE RADON TRANSFORM ON THE LAGUERRE HYPERGROUP

Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.

Low temperature J-resistance curve determination of asphalt concrete using wavelet-Radon transform

A single specimen test using the three point single edge notched beam configuration at low temperatures for obtaining hot mix asphalt （HMA） resistance curves is developed.Resistance curves are obtained for mixtures at six temperature levels of＋5,0,-5,-10,-15,and-20 ℃ and three binder contents of 4％,4.5％,and 5％.Crack extension increments during the test are measured by means of an image processing technique using Radon transform and feature extraction.All the specimens exhibit a rising R-curve,indicating ductility and toughening mechanisms in the ductile-quasi brittle fracture of the mixture.It is observed that the reduction of temperature results in a further tendency of the mixture for unstable crack growth and less subcritical crack length.It is also shown that using the binarization process,an automatic index can be developed that can represent the extent of brittleness and extent of the low temperature in which the cracking has occurred.

The Radon Transform on Tangent Space of Bounded Symmetric Domain SO~*(8)/U(4)

We study the Radon transform on the Cartan motion group associated with the bounded symmetric domain SO * (8)/U(4) , and prove that certain orbit of the regular elements is not the spectral synthesis set for the Fourier algebra on this Cartan motion group.

Application of the Regularization Method to the Numberical Inversion of a Class of Generalized Radon Transform

In the research of bistatic tomography imaging of translating object, we get a class of generalized Radon transformation. In this paper, first we prove the existence and uniguenness of its solution in theory and point out this problem is ill-posed with an especial example.Secondly by means of multiplicative interpolation functions to approximate models, we constracted regularizing functional. Finally we simplify calculation by Fourier transformation,get regularizing solutions that converge to accurate solution.