Hangyi Jiang

Techniques to improve the accuracy and to reduce the variance in noise power spectrum measurement

Several techniques to increase the accuracy and to reduce the variance of the noise power spectrum (NPS) measurement for digital X-ray imaging systems are investigated. These techniques include: (1) averaging the outputs from subblocks of the entire image; (2) averaging the two-dimensional NPS data along a circular route centered on the origin of spectral domain; and (3) masking a window function on each subblock before Fourier transforms. Techniques (1) and (2) are used mainly to reduce the variance of the NPS measurement. Technique (3) serves to improve the accuracy of the final result. Experiments with two different charge-coupled device-based X-ray imaging systems demonstrated that the precision and accuracy of the NPS measurement could be significantly improved using these techniques. The impact of the image partition for averaging is discussed and the corresponding NPS estimations are presented for the number of subblocks ranging from 4 to 64. The effect of masking on the NPS is also studied using four different window functions.

Lens distortion in optically coupled digital x-ray imaging

UNLABELLEDnThe objectives of this research are to analyze geometrical distortions introduced by relay lenses in optically coupled digital x-ray imaging systems and to introduce an algorithm to correct such distortions.nnnMETHODSnThe radial and tangential errors introduced by a relay lens in digital x-ray imaging were experimentally measured, using a lens-coupled CCD (charge coupled device) prototype. An algorithm was introduced to correct these distortions. Based on an x-ray image of a standard calibration grid, the algorithm first identified the location of the optical axis, then corrected the radial and tangential distortions using polynomial transformation technique.nnnRESULTSnLens distortions were classified and both radial and tangential distortions introduced by lenses were corrected using polynomial transformation. For the specific lens-CCD prototype investigated, the mean positional error caused by the relay lens was reduced by the correction algorithm from about eight pixels (0.69 mm) to less than 1.8 pixels (0.15 mm). Our investigation also shows that the fourth order of polynomial for the correction algorithm provided the best correction result.nnnCONCLUSIONSnLens distortions should be considered in position-dependent, quantitative x-ray imaging and such distortions can be minimized in CCD x-ray imaging by appropriate algorithm, as demonstrated in this paper.

A localization algorithm and error analysis for stereo x-ray image guidance

Stereo x-ray radiography attracts increasing attention in major clinical applications. The purpose of this paper is to analyze the 3D localization error for breast biopsy procedures and provide guidelines for improving its accuracy. Our prototype is a CCD based digital stereo x-ray imaging system. The mathematical model consists of two x-ray sources and one stationary detector plane. A closed form least-squares solution is derived for 3D localization of feature points, particularly a biopsy needle tip, from a pair of 2D digital radiographs. Based on the least-squares formula and its first order approximation, the 3D localization error is analyzed in terms of object location, measurement error, separation between the two x-ray sources, and distance from the source to the detector. The stereo imaging and error estimation formulas are numerically simulated and experimentally validated. The data are in agreement with theoretical prediction. These results can be used for the purpose of system design and protocol optimization.

Measurement of x-ray attenuation coefficients of aqueous solutions of indocyanine green and glycated chitosan

We report our experimental results of measurements of x-ray attenuation coefficients of aqueous solutions of a light absorbing dye, indocyanine green, and an immunoadjuvant, glycated chitosan. In the treatment of metastatic tumors in rats using a novel laser immunotherapy these solutions were administered in situ. The x-ray attenuation data of the solutions are essential to development of an x-ray digital imaging system for monitoring the administration of the solution, as well as for the distribution and the diffusion of the solution in tumors and in surrounding tissue. The composition of the solutions, the measurement system configuration, and the technique used to determine the attenuation coefficients are described. The experimental results show that glycated chitosan has a higher attenuation coefficient compared to indocyanine green and water. Our experimental data proved that, even at low concentrations, the x-ray attenuation through these aqueous solutions could be differentiated. Therefore, a digital x-ray imaging technique can be used effectively in monitoring and controlling the intratumor diffusion and distributions of these solutions.

Localization error analysis for stereo X-ray image guidance with probability method

The mean value and standard deviation of localization error for the stereo imaging systems are derived based on probability theory. Compared with the maximum error analysis method used in our previous study, the new approach yields more informative and precise results as the guidance for X-ray imaging system design and protocol optimization. The prototype for our current study is a CCD based monoplane digital stereo X-ray imaging system. The imaging model consists of two X-ray sources and one detector plane. With perspective geometry, the least-square solution is derived to reconstruct 3-dimensional object points, such as a biopsy needle tip, from a pair of 2-dimensional digital radiographs. Under the conditions of our specific prototype, the measurement errors of interested points in the radiographs are modeled as random variables with Gaussian distribution. Such variables account for finite image system noise and positioning errors. Then, the 3D localization error, in terms of mean value and standard deviation, is formulated using measurement error, feature point location, and separation between the two X-ray sources and distance from source to detector. Both theoretical analysis and numerical simulation are performed. The mean value and standard deviation of the localization error are first evaluated using numerical simulation under practical imaging conditions. Then, the error estimates are given in simply analytic forms. Simulation and theoretical results are in excellent agreement. The results show that our prototype X-ray stereological imaging system is accurate and reliable to locate feature points in 3D for medical intervention. Imaging protocols can be effectively optimized through the 3D localization error analysis using the approximate formulas proposed in this study.

Positional accuracy and sensitivity in x-ray stereo image guidance

A mathematical model for x-ray stereo-image guidance system is present in this paper. Based on this model, the relationship between 3D point and its 2D image projection is expressed as a 4 X 4 transformation matrix, which is composed by a series of coordinate transformations including translation, rotation and perspective projection. The principle method to recover 3D object position from stereo- image pairs is derived according to the system model we presented. The 3D object positional accuracy and system sensitivity of the x-ray stereo-image guidance system is discussed, and effectiveness of system incoherent parameter is revealed. The result shows that the absolute positioning error is proportion to the absolute position of the object under world coordinate system, and the system sensitivity is inversely proportional to the object position. Our result is very helpful to determine the system parameters in building a costly prototype. Such parameters include x-ray tubes separation, detector size, digital image resolution, SID and so on. The experiment was performed and the result was consistent with the expected value predicated by theoretic analysis. Our promising application of this method lies in digital mammography imaging guidance, but applications in other types of radiographic imagine are possible also.

Effect of window function on noise power spectrum measurements in digital x-ray imaging

Noise power spectrum (NPS) is an important parameter of x- ray imaging systems. Accurate and precise measurement of NPS is crucial in the system characterization. One method to improve the accuracy of the NPS measurement is to implement window functions, which fall off gradually at the edge of the images, before the Fourier transform of the noise intensity. Such window functions can reduce frequency leakage caused by sharp intensity change at the edge of an image. Three window functions, Bartlett, Hann, and Welch, were studied for their effects on the NPS measurement using two different digital x-ray imaging systems. The noise power spectra masked by window functions were also compared with that of no window (or square window) masking. Our results showed that the window functions reduced the high-frequency contribution to the noise power spectrum, hence improving the accuracy of its measurement. The relative errors of NPS using different window functions relative to NPS using Welch window function showed that the square window had the most fluctuation.

Characteristics of lens distortion and methods to correct geometrical distortion caused by lenses in optically coupled digital x-ray imaging: A response to Dr. E. H. B. M. Gronenschild’s comment

Dr. Gronenschild commented that our paper sho ‘‘...lack of awareness of current pertinent literature.’’ How ever, 3 of 4 articles he listed—Boone et al., 1991; Gronenschild, 1997; 3 and Fahrig, 1997 —were indeed referenced in our paper 1 as Refs. 10, 13, and 23. The fourth paper, Gro enschild, 1999, 5 was published after our paper was submitte and peer reviewed. With regard to his own publication, D Gronenschild commented that ‘‘...a more accurate and p cise method is presented in Gronenschild’’ ~Gronenschild, 1999!. However, this article concerns images acquired image intensifier based x-ray imaging systems. We wou like to emphasize that our article focused on geometri distortions caused by relay lenses. The digital x-ray imagi systems addressed in our paper use lenses to relay im from the scintillating screen to the electronic imager ~p. 911 in our paper !. The algorithm presented in our article is base on the nature and classification of lens distortion and correcting geometrical distortions caused by lenses in dig x-ray imaging. The distortion of relay lenses is differen from that of an image intensifier. One should not expect th the algorithms for correcting lens distortion are necessa consistent with the algorithms for image intensifier bas systems. For instance, the Comment argued that Carte coordinates should be used instead of polar coordinates. though this may be true for correcting distortion introduce by image intensifiers, lens-based optical systems are prin pally rotational symmetric and principally modeled in pola coordinates in the design/manufacturing process. Althou there exists nonrotational symmetric factors, a well design assembled lens is essentially rotational symmetric. The fore, it is convenient to model lens systems and to corr residual distortion using polar coordinates. The Comment argued that the method ~used in our paper ! is very sensitive to noise in the localization of the grid ca bration points, and also inferred that ‘‘any feature poi should have a corresponding feature point located symme cally opposite the center’’ otherwise ‘‘a bias is introduced. In response, we reiterate the robustness of the algorithm cussed in our paper which first detects a group of adjac pixels ~not a single pixel alone ! with lowest gray levels as the candidates of the grid calibration point ~p. 909 of our paper !. Although this method is not the only approach w considered, it has the merit of simplicity and has worke well in our experiences. Furthermore, our algorithm does n

Calibration technique for monoplane stereo x-ray system in imaging guidance

A simple calibration technique for monoplane stereo x-ray imaging system in stereotactic breast biopsy was developed. According to the principle of perspective projection, a monoplane stereo imaging model was established, the geometric parameters for the purpose of 3D point reconstruction were described. The parameters are source- imager-distance and the x-ray tube positions with respect to the imaging receptor. These parameters are calculated using a phantom consisting of three radio-opaque calibration lines of known length and orientation in 3D space and applying the concepts of similar triangles. Two line segments are parallel to the image detector and another one is perpendicular to the image detector. The computer simulations and experiments were carried out which determines these parameters for our CCD based monoplane stereotactic prototype. The results were in agreement with the theoretical prediction. This calibration technique is applied to the stereo imaging system where the final calibration error is within 1.5 percent. The method is simple and reliable. One promising application of this technique for the calibration lies in digital mammography imaging guidance, but applications in other forms of radiographic imaging are possible also.