Clinical diagnosis and security detection tasks increasingly require 3D information which is difficult or impossible to obtain from 2D (two dimensional) radiographs. As a 3D (three dimensional) radiographic and non-destructive imaging technique, digital tomosynthesis is especially fit for cases where 3D information is required while a complete projection data is not available. Nowadays, FBP (filtered back projection) is extensively used in industry for its fast speed and simplicity. However, it is hard to deal with situations where only a limited number of projections from constrained directions are available, or the SNR (signal to noises ratio) of the projections is low. In order to deal with noise and take into account a priori information of the object, a statistical image reconstruction method is described based on the acquisition model of X-ray projections. We formulate a ML (maximum likelihood) function for this model and develop an ordered-subsets iterative algorithm to estimate the unknown attenuation of the object. Simulations show that satisfied results can be obtained after 1 to 2 iterations, and after that there is no significant improvement of the image quality. An adaptive wiener filter is also applied to the reconstructed image to remove its noise. Some approximations to speed up the reconstruction computation are also considered. Applying this method to computer generated projections of a revised Shepp phantom and true projections from diagnostic radiographs of a patient’s hand and mammography images yields reconstructions with impressive quality. Parallel programming is also implemented and tested. The quality of the reconstructed object is conserved, while the computation time is considerably reduced by almost the number of threads used.
The presampling modulation transfer function (MTF) of a digital imaging system is commonly determined by measuring the system’s line spread function (LSF) using a narrow slit or differentiating the detector’s edge spread function (ESF) with an edge device. The slit method requires precise fabrication and alignment of a slit as well as a high radiation exposure. The edge method  is a complicated image processing procedure, requiring determination of the edge angle, reprojection, sub-binning, smoothing and differentiating the ESF, and spectral estimation. In this paper, a simple method is employed to evaluate the MTF using an edge device. The image processing procedures required by this method involve simply the determination of the over-sampling rate and the Fourier transform of the modified ESF. Differentiation and signal to noise ratio (SNR) improvement are jointly applied in the Fourier domain. The MTFs obtained by this simple method are compared to the theoretical MTF and the previously proposed more complicated edge method. The experimental results show that the proposed method provides a simple, accurate and convenient measurement of the presampling MTF for digital imaging systems.
In this paper, a fast, accurate and memory-saving Tomosynthesis algorithm is presented based on the Algebraic Reconstruction Technique (ART). In this approach, a one step ART iterative reconstruction takes the place of the commonly used two step Tomosynthesis reconstruction and deblurring processes. The weight matrix required by ART is calculated offline and saved in a look-up-table since the weight matrix will not change with the object if the acquisition geometries of the projections are fixed. This look-up-table speeds up the reconstruction procedure and the memory space is greatly reduced by using a compact weight matrix. A Bessel-Kaiser function is utilized in this algorithm as the pixel basis function, which improves the quality of the reconstruction over other commonly used basis functions. Simulation results show that the presented algorithm generates fast, accurate and memory-saving reconstructions of a three-dimensional object.
Traditional Tomosynthesis requires the X-ray source to be parallel beams or cone beams constrained to the same plane above the object of interest. Commonly, the X-ray sources are placed uniformly around a circle or along a line in the same plane, which demands fixed and high-precision equipment. To eliminate the constraints on the X-ray sources and obtain fast and efficient reconstruction with adequate quality, a fast and unconstrained cone beam Tomosynthesis reconstruction method as well as the corresponding deblurring method is presented in this paper. In this method, two reference balls, whose connecting line is parallel to the detector, are placed above the detector. According to the information provided by these two balls, the X-ray source position and its relative motion are readily calculated for the reconstruction and the corresponding deblurring processes. A layer-by-layer, rather than a voxel-by-voxel, reconstruction is utilized in order to speed up the calculation. This fast and unconstrained cone beam Tomosynthesis has a large commercial value, allowing unconstrained projection acquisition and making portable and relatively cheap Tomosynthesis equipment possible.