PRINCIPLES OF IMAGE RECONSTRUCTION IN CT - poonam rijal.pptx

COMPUTED TOMOGRAPHY RECONSTRUCTION

1. PRINCIPLES OF IMAGE RECONSTRUCTION IN CT PRESENTED BY POONAM RIJAL Bsc.MIT 2 ND Year Roll no. :- 154 Maharajgunj Medical Campus,IOM

2. Content Introduction Basic terminologies Simple back projection Analytical method Filtered back projection Fourier reconstruction Iterative reconstruction Statistical/hybrid iterative reconstruction Model based iterative reconstruction Deep learning reconstruction

3. Introduction It is a method of forming the CT image by manipulating the raw data obtained from the detector. Mathematical process to generate image data from different angle around the patient . Algorithm use attenuation data measured by detector & systematically buildup the image for viewing and interpretation. Computer intensive task and most crucial step in CT imaging process.

4. Basic P rinciple

5. Steps for CT image reconstruction All CT system uses a three step process :- scan or data acquisition - GET DATA Image reconstruction – USE DATA Image display – DISPLAY DATA

6. How CT image is formed ?

7. History Dates Events 1917 J. Radon (an Austrian mathematician ) presented mathematic solution for reconstruction as radon transform 1963 William H. Oldendorf developed a direct back projection method 1967 Bracewell and Riddle first proposed the idea of filter back projection 1970 Gordon et al. proposed the algebraic reconstruction technique (ART)

8. History Dates Events 1971 Convolution back projection algorithms developed by Ramachandran & Laxminarayan 1974 Shepp & Logan used convolution back projection to improve image quality & processing time 2009 The first iterative reconstruction technique was clini cally introduced 2019 Clinical Application of Deep Learning Reconstruction

9. Reconstruction Terminologies Ray :- the path that the x-ray beam takes from the tube to the detector at a given movement in a time is referred to a ray. Ray sum :- DAS reads each arriving ray and measured how much of the beam is attenuated the measurement is call ray sum. Projection: a series of rays that passes through the patient at the same orientation is called projection or a view . Many projections or views are required to create a CT image which consist of many scan lines called rays.

10. Raw Data All of the thousand of bits of data acquired by the system with each scan are called raw data/scan data . The process of using the raw data to create a image is called image reconstruction . Raw data includes all the measurement obtained from the detector array thus, a variety of images can be created by using the same data. Raw data requires vast amount of hard disk space , CT system offers limited disk space for the storage of raw data .

11. Image data computer assigns one value (Hounsfield unit ) to each pixel to form an image . The value is the average of all the attenuation measurement for that pixel . Once the raw data are averaged so that each pixel has one associated number image is formed and data obtained from the image is called image data. Image data required approximately one-fifth of the computer space needed for raw data. Data manipulation is limited in presence of only image data

12. Attenuation In computed tomography a cross-sectional layer of the body is divided into many tiny blocks, and then each block is assigned a number proportional to the degree that the block attenuated the x-ray beam . The individual blocks are called " voxels." Each voxel is assigned a number proportional to the degree of beam attenuated . Beam attenuation depends on linear attenuation coefficient . Their composition and thickness, along with the quality of the beam, determine the degree of attenuation .

13. N= N O e -(µ1+µ2+µ3+µ4+………µ i )x ( i is determined by matrix size)

14. CT number The relative attenuation coefficient is normally expressed in “Hounsfield unit “ which are also known as a “CT number”. Therefore each tissue element (voxel) is assigned by a “CT number“. The relation between linear attenuation coefficient and CT number is given by :- where , k = 1000 is a constant factor which determines the contrast scale, are linear coefficient of element tissue and water .

15. A lgorithm precise set of steps to be followed in specific order . Basis of computer programming. Thousands of equations must be solved to determine the linear attenuation coefficients of all the pixels in the image matrix. Reconstruction algorithms are used to solve the mathematical equations to convert information from detector array to image suitable for the display . CT reconstruction algorithms are divided into the three types :- Back projection Iterative method Analytical method

16. Sinogram The data acquired for an individual slice can be displayed before reconstruction . This type of display is called sinogram . Thus it is the 2D representation of the data obtained during a scan. Provides visual representation of x-ray attenuation values at each point within the object as the beam passes through it from different angles. Intensity measurement are done and then angle of projection (Rays) are plotted horizontally (x-axis) and views are shown on a vertical axis (y-axis) . During the 360 degree CT acquisition of a particular object, the position of the ray corresponding to that object varies sinusoidally as a function of the view angle .

17. AP

18. Gantry angle Attenuation profile 0º 180º

19. Sinogram The sinogram is useful for analyzing the raw projection data , flexibility in reconstruction in artifacts detection , inconsistencies and evaluating the quality of acquired data.

20. Convolution Mathematical filtering process of projected data by the mathematical filter to reduce blurring effect of projection Depending on manufacturer the mathematical filter may be called as Algorithm Convolution Filter Kernel Filter function applied to raw data

21. Parallel beam and Fan beam Every ray sum in fan beam sinogram has equivalent parallel beam sinogram The diverging ray is interpolated into a parallel ray sinogram For fan beam reconstruction, the previous parallel beam algorithms may be applied after we reformat fan beam projection into parallel beam projection which is known as Rebinning Reconstruction is performed as if data were collected in parallel beam geometry

22. Interpolation Mathematical method of estimating the value of a unknown function using the known value on either side of the function . Interpolation is used in CT in the image reconstruction process and the determination of slices in spiral/ helical CT imaging,

23. Image Reconstruction in H elical CT Reconstruction of Helical CT is same as conventional axial CT with interpolation Data interpolation is performed by a special program called as interpolation algorithm During Helical CT image data are received continuously but when image is reconstructed the plane of image doesn’t contain enough data for image reconstruction so, the data needed for image reconstruction is estimated by a special computation method known as Interpolation algorithm

24. Interpolation Reconstruct image at z-axis position through interpolation There are two types of interpolation algorithm 360º linear interpolation algorithm :- Plane of reconstructed image interpolated form data acquired on a revolution apart , thicker slice ,blurring in reforrmated image ,noise reduction 180º Linear interpolation algorithm :- Plane of reconstructed imageinterpolated form data acquired on a half revolution apart ,thinner slices ,increased noise improved resolution

25. Projected data from helical scanning sinogram Select interpolation points Linear interpolation for each projection angle Reconstruction algorithm Image data

26. Cone Beam A lgorithm The fan beam approximation algorithms are not very accurate used with the new generation of MSCT scanners, so other image reconstruction algorithms are needed. These algorithms are called cone-beam algorithm. ls in case of MDCT where the cone angle is larger resulting cone beam artifact The cone beam algorithm is developed to eliminate cone beam artifact

27. Fig: cone beam reconstruction are similar to standard fan beam reconstruction algorithms, but They keep track of the beam divergence in the Z- directioni.e cone angle direction Backprojection occurs as describes earlier, however, the algorithm computes the Backprojection angles in both the fan and cone angles.

28. There are two classes of cone beam algorithm with new generation of MSCT scanners :- Exact cone beam algorithm (computationally complex & difficult to implement) Approximate cone beam algorithm 3D Algorithm ( Fledkamp - Devis -Kress Algorithm) 2D Algorithm (Advanced Single-slice Rebinning Algorithm )

29. Preprocessing : Prior to Image R econstruction Various preprocessing procedures are applied to the actual acquired projection data prior to CT image reconstruction air calibration scans : the influence of bow tie filter is characterized , characterize the differences in individual detector response ,corrects previously identified inhomogeneity's in the field A dead pixel correction algorithm : replaces dead pixel data with interpolated data from surrounding pixels Scatter correction algorithms : Adaptive noise filtration methods algorithms; to reduce the impact of noise

30. Image display Image acquisition Image reconstruction Dead pixel correction algorithm :replace dead pixels with interpolated data from surrounding pixel Air calibration scan : characterize difference in individual detector reponse Adaptive noise filtration algorithm :reduce impact of noise

31. Methods of I mage Reconstruction Simple Back projection Analytical methods 1. Filtered Back projection 2 .Fourier transformation Iterative method 1. Statistical iterative reconstruction/ Hybrid Iterative Reconstruction(HIR) 2. Model based iterative reconstruction(MBIR)

32. Simple B ack Projection Also known as summation method It is the oldest reconstruction method. The term back projection is used because it reverses the process of acquiring the projection . Here the images are reconstructed if the average attenuated value of a certain body part are projected back on to the image area thus from attenuated value to a matrix.

33. Patient scan Acquisition of projected data through multiple angle Assign average attenuation values from each ray sum to corresponding pixel in image Pixel value are added up along the direction of the projection Repeated for each gantry angle Final back projection is sum of all back projected attenuation profiles

34. Backprojection image from a single projection

35. Simple B ack Projection Advantages :- Simple to understand Basis for modern image reconstruction technique Disadvantages :- no sharp images due to blurring effect Prone to artifacts (star type) Poor handling of noisy data

36. Analytical Method Creates high quality images from acquired projection . A mathematical technique known as convolution or filtering . It employs filter to remove blurring artifact. Two types :- Filtered back projection F ourier reconstruction

37. Filtered B ack projection It is similar to back projection except that the image is filtered to counterbalance the effect of star pattern . Projection data is applied with mathematical filter before back projection as a result the blurring faced during simple back projection is removed . The Mathematical filtering step involve convolving the projection data with a convolution “KERNEL ” on a spatial domain . Convolution filter refers to a mathematical filtering of the data designed to change the appearance of the image.

38. MEASUREMENT DATA PREPROCESSING RAW DATA CONVOLUTION FILTERED OR CONVOLUTED DATA BACK PROJECTION IMAGE DATA

39. Filters The primary purpose of the filter is to correct the blurring effect inherent in the back projection process and to control noise . Filter function is applied to the raw data . Various filter involves :- Ramp filter : ideal reconstruction filter , sensitive to noise S hepp - Logan filter: Ramp filter X Sinc function Cosine filter: Ramp filter X Cosine function Hamming window filter: Ramp filter X Hamming window Hann window filter: Ramp filter X Han window

40. Filters Ramp filter : It amplifies high-frequency components linearly, which helps in sharpening the image. While it enhances edge definition, it can also amplify noise significantly Shepp -Logan Filter : A modification of the Ram-Lak filter that includes a sinc function to reduce noise with still enhancing edges. Cosine filter : gradually attenuates higher frequency Provides smoother images with reduced noise but slightly less sharpness compared to the Ramp filter

41. Filters Hamming Filter : A filter that smooths the high-frequency components to reduce noise at the cost of some resolution. Hann Filter : Similar to the Hamming filter, it provides a compromise between resolution and noise reduction Produces very smooth images with significant noise reduction, but can lead to loss of fine details

42. HIGH PASS FILTER Keeps edge information intact Ramp & Shepp – Logan filter Commercially named as Ultrasharp, Sharp, Bone Gantry angle Attenuation profile 0º 180º

43. LOW PASS FILTER Also known as band pass filter Smooth the image & reduce noise Cosine filter, Hamming filter, Hann filter Commercially named as Soft tissue, Standard Gantry angle Attenuation profile 0º 180º

44. SHARPNESS SMOOTHNESS

45. Vendors Specific Filters SIEMENS RECONSTRUCTION KERNEL Siemens kernel have four position : ( Kernal type, Resolution, version, Scan mode) Kernel type: B: Body, C: Child head, H: Head, U: Ultrahigh resolution, S: Special kernel, T: Topogram Resolution : 1, 2, 3, 4, 5, 6, 7, 8, 9 (Higher number high resolution & vice versa) Version : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Scan mode: f: fast, s: standard, h: high resolution, u: ultrahigh resolution

46. GE RECONSTRUCTION KERNEL Soft Standard Detail Lung Bone plus Edge SIMENS RECONSTRUCTION KERNEL The available kernel are B10 – B90 for Body H10 – H90 for Head U30 – U90 for Ultrahigh resolution T20 – T81 for Topogarm Lower number smoother Middle number standard Higher number sharper

47. Advantages of F iltered B ack P rojection Simple & easy to understand Rapid reconstruction & suitable for real time or near real time image reconstruction Require fewer computational resources compared to advanced iterative reconstruction algorithms Improved image quality but lower than that of iterative reconstruction The characteristics of FBP reconstructed image data are user controlled (specific choice of reconstruction kernel resulting image of well known noise structure & texture)

48. Disadvantages of Filtered B ack P rojection FBP can amplify noise, especially in low-dose CT scans. The high-frequency components enhanced by the filters can also enhance noise, leading to grainy images. . Any deviation in the acquisition data can produce dramatic image artifacts, such as streak or ring artifacts. FBP offers negligible dose reduction potential.

49. Fourier Reconstruction A radiograph can be considered an image in the spatial domain;ie shades of grey represents various parts of the anatomy ( e.g..,bone is white and air is black)in space. With FT , this spatial domain image –the radiograph represented by the function f( x,y ) can be transformed into a frequency domain image represented by the function f( u,v ).

50. Fourier transform The Fourier transform is a mathematical operation that transforms a function of time (or space) into a function of frequency. This is particularly useful for analyzing the frequency components of signals

51. Steps for F ourier Reconstruction The object to be scanned is represented by the function f( x,y ) Projection data are obtained from the object . A projection dataset for at least a 180 degree rotation is required for adequate reconstruction.These projections represent a spatial domain image. Each projection is transformed into the frequency domain by the fourier transform.These image must be converted into a clinically useful image. Because ct scanners use FFT developed specifically for digital implementation,the frequency domain image must be placed on a rectangular grid. Finally,the interpolated image is transformed into a spatial domain image of the object through an inverse fourier transform operations

52. Advantages of Fourier reconstruction The image in the frequency domain can be manipulated( e.g..,edge enhancement or smoothing)by changing the amplitude of frequency components. Computer can perform those manipulations (digital image processing). Frequency information can be used to measure image quality through point spread function, line spread function, and modulation transfer function

53. Iterative R econstruction Iterative refers to “repetition” It is also called successive approximation method or correction method. The Algebraic Reconstruction Technique (ART) was the first iterative reconstruction technique used for  computed tomography  by  Hounsfield. This method starts with the assumption that all points in the matrix along the ray have the same value. This assumption is compared with the measured value and make correction to bring the two into agreement. Iterative reconstruction attempts to find the image that is the “best fit” to the acquired data.

54. Iterative Reconstruction Generic Steps: Assumption : (for example all points in the matrix have same value) Comparison: (with the measured values) Correction(to bring the two into agreement) Repetition(of the process until the assumed and measured values are the same or within acceptable limit

55. Image with low exposure technique Reduced image noise and artifact Preserve image quality Undergoes Iterative reconstruction Low radiation dose to the patient Image with higher noise and artifact

56. I terative Reconstruction Iterative reconstruction is divided into two types :- Statistical or Hybrid iterative reconstruction :- HIR Model based iterative reconstruction :- MBIR

57. Statistical/Hybrid I terative R econstruction used originally by Godfrey Hounsfield, however not commercially used due to the inherent limitations of microprocessors at that time Term system statistics refers to the photon spectrum emitted by the x-ray tube, the statistical distribution of photons & the noise of detector electronics Characterized by iterative filtration of data separately performed in projection or image space to reduce noise Actual image reconstruction relies on filter back projection so termed Hybrid iterative reconstruction The speed of iterative reconstruction is comparable to FBP

58. Hybrid Iterative R econstruction Image data iteratively filtered Iteratively filtered Reduce noise Reduce artifacts Backprojection Projection data

59. Advantages of HIR Higher image quality compared to FBP particulary in terms of noise reduction and artifact suppression but less than MBIR. Less computational time so quick processing speed. Requires less power less energy consumption. Uses simpler algorithm making it easy to implement and optimize. Lower cost

60. Disadvantage of HIR Moderate noise reduction and image quality as compared to MBIR but higher than FBP. Although less demanding than MBIR, HIR still requires more computational resources than traditional FBP

61. VENDOR SPECIFIC STATISTICAL ITERATIVE RECONSTRUCTION Hybrid IR Vendor AIDR 3D Adaptive Iterative Dose Reduction 3D Canon Medical Systems ASIR Adaptive Statistical Iterative Reconstruction GE Healthcare ASIR - V Adaptive statistical iterative reconstruction - V GE Healthcare iDose4 Philips Healthcare SAFIRE Sinogram- Affirmed Iterative Reconstruction Siemens Healthineers

62. Model Based I terative R econstruction To overcome the limitations of FBP, MBIR was introduced for clinical use in 2009 . MBIR is the most computationally demanding type of IR because it uses multiple iterations of forward and back projections between the sinogram domain and image domain to optimize image quality. It aims to produce highly accurate and high-quality images by iteratively refining the image based on comprehensive modeling of the entire imaging system . Models of the acquisition process, noise statistics, and system geometry reconstruct the projections as accurately as possible..

63. Model Based I terative R econstruction The more complete model of MBIR allows for more reduction of noise and artifacts than FBP does However, the high computational requirements and long reconstruction times of MBIR have limited its widespread clinical application.

64. Projection data Backprojected into image space Image space data forward projected Artificial projection data Compared to true projection data Update the image with noise reduction Model B ased I terative R econstruction iteratively refine the image based on comprehensive modeling of the entire imaging system

65. Advantages of MBIR In terms of image quality and noise reduction, MBIR>HIR>FBP In terms of reduced patient dose , , MBIR>HIR>FBP Higher SNR Better artifact suppression high diagnostic accuracy uses detailed models of the CT system, including the geometry of the scanner, the X-ray tube, and detector characteristics, leading to more accurate image reconstruction .

66. Disadvantage of MBIR MBIR requires extensive computational resources, leading to longer processing times compared to traditional methods like FBP and HIR. Powerful computational hardware requirement increasing cost and complexity.

67. VENDOR SPECIFIC MODEL BASED ITERATIVE RECONSTRUCTION Model Based IR Vendor ADMIRE Advanced modeled Iterative Reconstruction Siemens Healthineers FIRST Forward Projected Model – Based Iterative Reconstruction Solution Canon Medical System IMR Iterative Model Reconstruction Philips Healthcare VEO (MBIR) GE Healthcare

68. SAFIRE sinogram affirmed iterative reconstruction Introduced in 2010 by Siemens Healthineers Utilizes both projection (raw data) & image data Reconstruct 20 images/ second In comparison to FBP Dose: 60% ↓ Image noise: ≈35%↓ SNR: ≈50% ↑ five different strength defining parameter of the underlying noise model/ regularization (SAFIRE 1 – 5)

69. Deep L earning Reconstruction   It uses AI technology to reconstruct a CT image. DLR is the combination of AI & supercomputing (Higher computing power ) DLR uses artificial intelligence to reconstruct high-quality images from lower-dose CT faster than MBIR DLR algorithm can be applied in both the raw data domain & image domain or both DLR potentially allows for radiation dose reductions between 30% and 71% compared with HIR while maintaining diagnostic image quality due to improved noise reduction.

70. Deep Learning Reconstruction Lower noise (30% - 70% ↓ compared to HIR & 50% ↓ compared to FBP) High SNR Increased spatial resolution Low radiation dose (30% - 71%↓ compared to HIR) Fast reconstruction speed Reconstructed image more natural in appearance than MBIR & HIR (image texture preserved) Higher metal artifact reduction

71. Summary Image reconstruction is the mathematical process of displaying CT image from the raw data obtained from the detector . There re generally three methods of image reconstruction :- Simple Back projection Analytical methods 1. Filtered Back projection 2.Fourier transformation Iterative method Hybrid iterative reconstruction Model based iterative reconstruction

72. References Seeram , E.  Computed tomography: Physical Principles, Clinical Applications, and Quality Bushberg ., 2012.  Essential Physics of Medical Imaging, The . Lippincott, Williams & Wilkins. Stewart C. Bushong -Radiologic Science for Technologists_ Physics, Biology, a CT for technologist Williams and wilkins Chrinstensen physics of diagnostic radiology Deep Learning Image Reconstruction for CT: Technical Principles and Clinical Prospects Filtered BackProjection (FBP) Illustrated Guide For Radiologic Technologists • How Radiology Works https ://www.dspguide.com/ch25/5.htm https://chat.openai.com/ Previous presentations

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