Compton imaging with 3d position sensitive detectors jiyang chu, michael streicher, jeffrey a. Pdf a quantitative comparative study of back projection. Out of all this approaches, a filtered backprojection method is presented in this article. Results the ct numbers and the contrasttonoise ratios were reported and how they are affected by the kernel choice and strength of iterative reconstruction. Fanbeam filteredbackprojection reconstruction without backprojection weight article pdf available in physics in medicine and biology 5211.
Iterative reconstruction noise suppression allows the use of lowerdose techniques with maintained image. Filtered backprojection perform for all projection. Illustration of the filtered backprojection fbp algorithm used in spect cameras. Similarly, think a 90degree projection would look like this. Filter design for filtered backprojection guided by the interpolation. Computed tomography image reconstruction presented by. Filtered backprojection direct backprojection results in blurred image could filter deconvolve resulting 2d image linear systems theory suggests order of operations unimportant filter projection profiles prior to back projection yet another alternative, and the one that is almost universallyemployed.
Modelbased iterative reconstruction versus adaptive. Methods five different scans were performed at 6 different tube potentials on the same catphan 600 phantom using approximately the same dose level and otherwise identical settings. The projections of these sources at 45 degree intervals are represented on the sides of an octagon. Conebeam reconstruction using filtered backprojection. Filtered back projection radiology reference article. This noniterative expression of the landweber algorithm resembles a backproject first, then filter algorithm, in the sense that the projection data p are first backprojected by the operator a t and then filtered by.
Fbp was the method of choice for decades, until the first iterative reconstruction ir technique was clinically introduced in 2009. Secondly, the resulting image is severely blurred, as shown in the figures below. How different iterative and filtered back projection. In contrast, in the case of the filtered backprojection fbp algorithm derived below, a basic realspace implementation with a simple convolution and a simple interpolation in the backprojection works well. Filtered back projection is an analytic reconstruction algorithm designed to overcome the limitations of conventional back projection. Comparison with standard filtered backprojection a. For example, general electric ge, milwaukee, wi, usa has introduced adaptive statistical iterative reconstruction asir, which uses a blend of filtered backprojection images with iteratively reconstructed images. We address here the interior problem in local tomography, by means of filtered backprojection fbp. Oct 30, 2018 the first ct scanners in the early 1970s already used iterative reconstruction algorithms. Through geometric analysis, a target optimization model was established.
Ct problems, filtered back projection, svd analysis. This is due to the fact that many different images are being overlapped in this area. Contrastmultiphasescans were performed on a 64section ct scanner. Fbp in medical imaging has provided a fast solution for image reconstruction, and has been widely used in many fields, such as pet, spect, etc. Lowdose head ct protocols using filtered back projection are susceptible to increased noise and decreased image quality. Exercises on the radon transform and the filtered back. The first ct scanners in the early 1970s already used iterative reconstruction algorithms. This algorithm, traditionally used in the context of complete. We consider using spline interpolation to improve the standard filtered backprojection fbp tomographic reconstruction algorithm.
Within a few years, all major ct vendors introduced ir algorithms for. Lets assume that we have a finite number of projections of an. Ct reconstruction package file exchange matlab central. That is, each of the onedimensional views is convolved with a onedimensional filter kernel to create a set of filtered views. The video contains the acquisition process transformation from image space to sinogram space. Im trying to write my own matlab code to compute the inverse radon transform iradon and thus far i have managed to successfully reconstruct an image using a ramp filter, a hamming window, and also. Comparison of iterative model reconstruction versus filtered. Filtered backprojection as a concept is relatively easy to understand. Filtered backprojection is a technique to correct the blurring encountered in simple backprojection.
In this paper the filtered back projection fbp algorithm is applied, fbp is considered to be the most common type of the analytical reconstruction methods. The evolution of image reconstruction for ctfrom filtered. Filtering refers to altering the projection data before we do the backprojections. Comparison of image quality between filtered backprojection. Ir has recently demonstrated its capacity to reduce noise and permit dose reduction in abdominal and thoracic ct applications. The purpose of this study is to develop an improved filtered. Aug 29, 20 simplified illustration of the principles of image reconstruction for ct scanners, using the standard filtered back projection method.
Filtered back projection vs adaptive statistical iterative. Image quality assessment of standard and lowdose chest ct. A filtered backprojection algorithm with characteristics of. The direct back projection is not the inversion of radon transform but just a back projection of the radon transform of the attenuation coefficient distribution. A conebeam ct reconstruction application is provided which implements filtered back projection using the feldkamp, davis, and kress fdk algorithm. Filtered backprojection method and the interior problem in 2d. R radoni,theta the number of samples per projection angle sqrt2 n iradon. The results are added together and the process repeated. Feb 07, 2012 illustration of the filtered back projection fbp algorithm used in spect cameras. It utilizes simultaneous equations of ray sums taken at differing angles of a sine wave to compute the values of. What is the problem when using filtered backprojection in. Then, the filtered projections are reconstructed using a backprojection algorithm. Based on a given data file containing fan beam xray data, a program has been created to perform ct reconstruction on the data.
If a function represents an unknown density, then the radon transform represents the projection data obtained as the output of a tomographic scan. It was, up until recently the primary method in cross sectional image reconstruction. Pdf use of filtered backprojection methods to improve. Set of functions performing ct reconstruction tasks like a radon transformation, a simple backprojection, a filtered backprojection using a convolution in the spatial domain, a filtered backprojection using a 2d fourier transformation, and a filtered. Iterative reconstruction noise suppression allows the use of lowerdose techniques with maintained image quality. Simplified illustration of the principles of image reconstruction for ct scanners, using the standard filtered backprojection method. Backprojection from projection matrix using matlab stack. First, it produces an image which has a high density in the center. Each projection is back projected onto the object plane. Traditional filtered back projection fbp has given way to novel iterative reconstruction algorithms, and its use has increasingly been employed. Summation of conebeam projections on the unit sphere. Filtered backprojection methods rely on mathematical transforms fourier, radon in order to provide more accurate results that can be obtained in much less. The parallel beam filtering backprojection algorithm was used to solve the problem based on the information received by the detector unit. The filtered backprojection or filtered back projection is an algorithm to reconstruct 2d image data from a set of available 1d projections.
How different iterative and filtered back projection kernels. The filter is designed directly in the frequency domain and then multiplied by the fft of the projections. Each scan is reconstructed in all three reconstruction algorithms. A conebeam ct reconstruction application is provided which implements filtered backprojection using the feldkamp, davis, and kress fdk algorithm. Pdf filtered back projection algorithm fbp is one of the most common methods that used in to mographic image reconstruction. Noncontrast ct of the head is the initial imaging test for traumatic brain injury, stroke, or suspected nonaccidental trauma. Image reconstruction for ct scanner by using filtered back. Exercises on the radon transform and the filtered backprojection algorithm jakob sauer j. Isbn 9172199199 issn 03457524 printedinswedenbyunitryck,link. Fessler, fellow, ieee, and zhong he, senior member, ieee abstractin compton imaging, iterative methods provide good performance but are usually computationally intensive. Reconstruction using back projection allows better resolution than interpolation method described above. Lowdose head ct protocols using filtered backprojection are susceptible to increased noise and decreased image quality. Filtering refers to altering the projection data before we do the back projections. Pdf use of filtered backprojection methods to improve ct.
Computed tomography the evolution of image reconstruction for ctfrom filtered back projection to artificial intelligence martin j. Image quality assessment of standard and lowdose chest. Reconstruction of images using filtered backprojection. Backprojection definition of backprojection by medical. The filter used does not contain dc gain, thus adding dc bias may be desirable. Make fourier transform of projected data apply filter in fourier domain make invers transform backproject and sum with previous image 19x center for fast ultrasound imaging, department of electrical engineering technical university of denmark.
Pdf the use of filtered back projection algorithm for. Input images in either raw, pfm, or hnd format are read, filtered, and back projected into a userdefined volume geometry. It is known that traditional computed tomography ct reconstruction algorithms, for example, filtered backprojection methods, are not compatible to laterally truncated projection data, which appears often in the case of either 1 when the object extends outside of the field of view fov or 2 xray beam collimation for the purpose of dose. Hence the inverse of the radon transform can be used to reconstruct the original density from the projection data, and thus it forms the mathematical underpinning for tomographic reconstruction, also known as iterative reconstruction. Now imagine back projection of these coordinates across your image, it would look something like this. The video contains the acquisition process transformation from image space to sinogram space done by the.
Pdf fanbeam filteredbackprojection reconstruction without. It utilizes simultaneous equations of ray sums taken at differing angles. Fbp filtered back projection, mbir modelbased iterative reconstruction, roi region of interest. This paper used the relevant knowledge of electronic computer tomography image reconstruction to solve the problem of ct system parameter calibration and imaging algorithm. Centres that have this technology use a varying degree of asir with most adopting a value between a 20 and 40 % asir blend. Im trying to write my own matlab code to compute the inverse radon transform iradon and thus far i have managed to successfully reconstruct an image using a ramp filter, a hamming window, and also using convolution of the 1d projections in the spatial domain with a window h in my code based on the textbook by kak and shakey. May 21, 2009 computed tomography image reconstruction presented by. A quantitative comparative study of back projection, filtered back projection, gradient and bayesian reconstruction algorithms in computed tomography ct. In fact, it took until 2009 for the first iterative reconstruction algorithms to come commercially available and replace conventional filtered back projection. This plane is then rotated through the appropriate angle and the next projection back projected. Only filtered back projection fbp at ni 33, adaptive statistical iterative reconstruction asir at ni 33 with 30% blending, and modelbased iterative reconstruction mbir at nis 60 and 70 were used for subjective analysis.
The filtered backprojection fbp algorithm is simple and fast, and can be used to reconstruct images in nuclear medicine and xray ct. Fessler, fellow, ieee, and zhong he, senior member, ieee abstractin compton imaging, iterative methods provide good performance. Mean attenuation differences across nine different reconstruction algorithms were analyzed using repeatedmeasures analysis of variance with dunnette posttest for multiple comparison using asir at ni 33 as a control. Twodimensional statistical model for regularized backprojection in. The scans were reconstructed using all available filtered back projection body kernels and with iterative reconstruction techniques. Mathematically it is based on the discrete inverse radon transform. Objective the aim of this study was to evaluate how different iterative and filtered back projection kernels affect the computed tomography ct numbers and low contrast detectability.
As you may have noticed, backprojection smears or blurs the final image. Pdf image reconstruction for ct scanner by using filtered. In order to fix the blurring problem created by standard backprojection, we use filtered backprojection. Imagine the axis youre projecting on has units 1,256. It was, up until recently the primary method in crosssectional imaging reconstruction.
Filtered backprojection in compton imaging 2789 fig. For example, general electric ge, milwaukee, wi, usa has introduced adaptive statistical iterative reconstruction asir, which uses a blend of filtered back projection images with iteratively. Input images in either raw, pfm, or hnd format are read, filtered, and backprojected into a userdefined volume geometry. A filtered backprojection algorithm with characteristics. Back projection 2d points to 3d cornell university. Applications are computed tomography, pet or quantum tomography. The parallel beam filtering back projection algorithm was used to solve the problem based on the information received by the detector unit. Based on the radon transform it outperforms the classical euclidean. Pdf use of filtered backprojection methods to improve ct image. Use results to constrain earthquake dynamics coherence between data and synthetics finiteslip inversions backfigure from chen ji projection. Lets assume that we have a finite number of projections of an object which contains radioactive sources fig. Computed tomography part i electrical and computer engineering.
The algorithm for back projection is just a variation of that for rotating a cartesian array. Since then, this technique has caused a true hype in the field of radiology. The name back projection comes from the fact that 1d projection needs to be filtered by 1d radon kernel back projected in order to obtain a 2d signal. Filtered backprojection in matlab and designing filter. Tomography interpreted as a filtered back projection rays. Ct image reconstruction method based on filtered back. Additionally, this inverse is optimized to perform better in realworld applications. Image reconstruction for ct scanner by using filtered back projection approach.
1266 418 1386 1232 1494 588 1062 1418 612 1 1446 746 495 211 1201 37 128 1288 1350 1575 559 761 168 233 1096 50 1173 511 1061 252 105 1144 640 51 414 398 269 1458