Inverse Radon Research Articles

Determination of singular value truncation threshold for regularization in ill-posed problems

Appropriate regularization parameter specification is the linchpin for solving ill-posed inverse problems when regularization method is applied. This paper presents a novel technique to determine cut off singular values in the truncated singular value decomposition (TSVD) methods. Simple formulae are presented to calculate the index number of the singular value, beyond which all the smaller singular values and the corresponding vectors are truncated. The determination method of optimal truncation threshold is firstly theoretically inferred. Two-dimensional inverse problems processing Radon transform are then exemplified. Formulae to solve the problem with insufficient image resolution and projection angle number are derived by the currently proposed method. The results show that accuracy of the current method is similar to that of TSVD but with much superior efficiency. On the other hand, insufficiency in input data affects the output accuracy of the inverse solution, a least square method can be engaged to establish formulae calculating the truncation threshold. For an insufficient set of input data, the percentage difference between inversely reconstructed signal and TSVD reconstructed signal is about 3%. The current formulae offer reliable and more efficient approach to calculate the truncation threshold when TSVD is applied to solve inverse problems with known system characteristics.

Inverse Radon transform and the transverse-momentum dependent functions

We revisit the standard representation of the (inverse) Radon transform which is well-known in the mathematical literature. We extend this representation to the case involving the parton distributions. We have found the new additional contribution which is essentially related to the generalized transverse-momentum dependent parton distribution and double-distribution functions. We discuss the possible relationship of this term with the Sivers function.

Piezoelectric line detector array for photoacoustic tomography

Photoacoustic tomography relies on a dense coverage of the surface surrounding the imaged object with ultrasound sensors in order to enable an accurate reconstruction. A curved arrangement of integrating line sensors is proposed that is able to acquire data for a linear projection image of the absorbed energy density distribution in the object. Upon rotation of the object relative to the array, three-dimensional (3D) images can be obtained.The proposed design is based on the cost-effective piezoelectric polymer film technology with 64 line shaped sensors arranged on a half-cylindrical surface. It is combined with an optical parametric oscillator for the near infrared as a source for laser pulses. Image reconstruction from recorded signals consists of two-dimensional (2D) back projection followed by an inverse Radon transform.The tomograph exhibits a spatial resolution on the order of 200 to 250μm. In a phantom experiment, the steps from acquisition of a single, 2D projection image to a full 3D image are demonstrated. Finally, in vivo projection images of a human finger are shown, revealing the near real-time imaging capability of the device in 2D.

逆合成孔径成像激光雷达实包络成像算法

Limited by laser modulation technology and the phase information that is easily damaged by atmospheric turbulence,it is difficult to obtain the 2-D high-resolution image using traditional coherent integration algorithms for Inverse Synthetic Aperture Imaging Lidar(ISAIL).To solve this problem,a real envelope imaging algorithm was proposed based on inverse Radon transform.Using the proposed method,the ISAIL system can transmit noncoherent laser pulses and high-quality image can also be obtained under the condition of atmospheric turbulence with low pulse repetition frequency.The ISAIL imaging experiment with numerical data validates the feasibility and effectiveness of the proposed method.