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61-457: The superiorization methodology is very general and has been used successfully in many important practical applications, such as iterative reconstruction of images from their projections, single-photon emission computed tomography , radiation therapy and nondestructive testing , just to name a few. A special issue of the journal Inverse Problems is devoted to superiorization, both theory and applications. An important case of superiorization

122-562: A 0.2 mm resolution. With modern dual-energy CT scanners, new areas of use have been established, such as aiding in the diagnosis of gout . CT is used in biomechanics to quickly reveal the geometry, anatomy, density and elastic moduli of biological tissues. Industrial CT scanning (industrial computed tomography) is a process which uses X-ray equipment to produce 3D representations of components both externally and internally. Industrial CT scanning has been used in many areas of industry for internal inspection of components. Some of

183-413: A Poisson likelihood function only. As another example, it is considered superior when one does not have a large set of projections available, when the projections are not distributed uniformly in angle, or when the projections are sparse or missing at certain orientations. These scenarios may occur in intraoperative CT, in cardiac CT, or when metal artifacts require the exclusion of some portions of

244-437: A better, but computationally more expensive alternative to the common filtered back projection (FBP) method, which directly calculates the image in a single reconstruction step. In recent research works, scientists have shown that extremely fast computations and massive parallelism is possible for iterative reconstruction, which makes iterative reconstruction practical for commercialization. The reconstruction of an image from

305-544: A continuously updated Internet page. SNARK14 is a software package for the reconstruction if 2D images from 1D projections that has a built-in capability of superiorizing any iterative algorithm for any merit function. Iterative reconstruction Iterative reconstruction refers to iterative algorithms used to reconstruct 2D and 3D images in certain imaging techniques. For example, in computed tomography an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are usually

366-520: A full roll-out on 1 December 2022 and the TSA spent $ 781.2 million on an order for over 1,000 scanners, ready to go live in the summer. X-ray CT is used in geological studies to quickly reveal materials inside a drill core. Dense minerals such as pyrite and barite appear brighter and less dense components such as clay appear dull in CT images. Traditional methods of studying fossils are often destructive, such as

427-444: A key role in the fast-evolving field of transcatheter structural heart interventions , more specifically in the transcatheter repair and replacement of heart valves. The main forms of cardiac CT scanning are: To better visualize the anatomy, post-processing of the images is common. Most common are multiplanar reconstructions (MPR) and volume rendering . For more complex anatomies and procedures, such as heart valve interventions,

488-450: A large variety of algorithms, but each starts with an assumed image, computes projections from the image, compares the original projection data and updates the image based upon the difference between the calculated and the actual projections. The Algebraic Reconstruction Technique (ART) was the first iterative reconstruction technique used for computed tomography by Hounsfield . The iterative sparse asymptotic minimum variance algorithm

549-411: A lower cost of production and purchase. The main limitation of this type of CT is the bulk and inertia of the equipment (X-ray tube assembly and detector array on the opposite side of the circle) which limits the speed at which the equipment can spin. Some designs use two X-ray sources and detector arrays offset by an angle, as a technique to improve temporal resolution. Electron beam tomography (EBT)

610-427: A mix of for example coloring and shading in order to create realistic and observable representations. Two-dimensional CT images are conventionally rendered so that the view is as though looking up at it from the patient's feet. Hence, the left side of the image is to the patient's right and vice versa, while anterior in the image also is the patient's anterior and vice versa. This left-right interchange corresponds to

671-473: A rotating X-ray tube and a row of detectors placed in a gantry to measure X-ray attenuations by different tissues inside the body. The multiple X-ray measurements taken from different angles are then processed on a computer using tomographic reconstruction algorithms to produce tomographic (cross-sectional) images (virtual "slices") of a body. CT scans can be used in patients with metallic implants or pacemakers, for whom magnetic resonance imaging (MRI)

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732-446: A slice. The table then increments again, and another slice is taken. The table movement stops while taking slices. This results in an increased time of scanning. Spinning tube, commonly called spiral CT , or helical CT, is an imaging technique in which an entire X-ray tube is spun around the central axis of the area being scanned. These are the dominant type of scanners on the market because they have been manufactured longer and offer

793-416: A true 3D reconstruction or a 3D print is created based on these CT images to gain a deeper understanding. CT is an accurate technique for diagnosis of abdominal diseases like Crohn's disease , GIT bleeding, and diagnosis and staging of cancer, as well as follow-up after cancer treatment to assess response. It is commonly used to investigate acute abdominal pain . Non-enhanced computed tomography

854-413: A very high dynamic range which must be reduced for display or printing. This is typically done via a process of "windowing", which maps a range (the "window") of pixel values to a grayscale ramp. For example, CT images of the brain are commonly viewed with a window extending from 0 HU to 80 HU. Pixel values of 0 and lower, are displayed as black; values of 80 and higher are displayed as white; values within

915-481: Is contraindicated . Since its development in the 1970s, CT scanning has proven to be a versatile imaging technique. While CT is most prominently used in medical diagnosis , it can also be used to form images of non-living objects. The 1979 Nobel Prize in Physiology or Medicine was awarded jointly to South African-American physicist Allan MacLeod Cormack and British electrical engineer Godfrey Hounsfield "for

976-530: Is a specific form of CT in which a large enough X-ray tube is constructed so that only the path of the electrons , travelling between the cathode and anode of the X-ray tube, are spun using deflection coils . This type had a major advantage since sweep speeds can be much faster, allowing for less blurry imaging of moving structures, such as the heart and arteries. Fewer scanners of this design have been produced when compared with spinning tube types, mainly due to

1037-406: Is a specific form of CT to assess flow through blood vessels whilst injecting a contrast agent . Blood flow, blood transit time, and organ blood volume, can all be calculated with reasonable sensitivity and specificity . This type of CT may be used on the heart , although sensitivity and specificity for detecting abnormalities are still lower than for other forms of CT. This may also be used on

1098-408: Is a two dimensional unit based on the matrix size and the field of view. When the CT slice thickness is also factored in, the unit is known as a voxel , which is a three-dimensional unit. Water has an attenuation of 0 Hounsfield units (HU), while air is −1,000 HU, cancellous bone is typically +400 HU, and cranial bone can reach 2,000 HU. The attenuation of metallic implants depends on

1159-405: Is a type of contrast CT to visualize the arteries and veins throughout the body. This ranges from arteries serving the brain to those bringing blood to the lungs , kidneys , arms and legs . An example of this type of exam is CT pulmonary angiogram (CTPA) used to diagnose pulmonary embolism (PE). It employs computed tomography and an iodine-based contrast agent to obtain an image of

1220-472: Is also under consideration for automated baggage/parcel security scanning using computer vision based object recognition algorithms that target the detection of specific threat items based on 3D appearance (e.g. guns, knives, liquid containers). Its usage in airport security pioneered at Shannon Airport in March 2022 has ended the ban on liquids over 100 ml there, a move that Heathrow Airport plans for

1281-400: Is an iterative, parameter-free superresolution tomographic reconstruction method inspired by compressed sensing , with applications in synthetic-aperture radar , computed tomography scan , and magnetic resonance imaging (MRI) . There are typically five components to statistical iterative image reconstruction algorithms, e.g. In learned iterative reconstruction, the updating algorithm

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1342-560: Is called high resolution CT that produces a sampling of the lung, and not continuous images. Bronchial wall thickening can be seen on lung CTs and generally (but not always) implies inflammation of the bronchi . An incidentally found nodule in the absence of symptoms (sometimes referred to as an incidentaloma ) may raise concerns that it might represent a tumor, either benign or malignant . Perhaps persuaded by fear, patients and doctors sometimes agree to an intensive schedule of CT scans, sometimes up to every three months and beyond

1403-502: Is done while retaining the feasibility-seeking nature of the algorithm and without paying a high computational price. Furthermore, general-purpose approaches have been developed for automatically superiorizing iterative algorithms for large classes of constraints sets and merit functions; these provide algorithms for many application tasks. The superiorization methodology and perturbation resilience of algorithms are reviewed in, see also. Current work on superiorization can be appreciated from

1464-458: Is how to reduce the radiation dose during CT examinations without compromising the image quality. In general, higher radiation doses result in higher-resolution images, while lower doses lead to increased image noise and unsharp images. However, increased dosage raises the adverse side effects, including the risk of radiation-induced cancer – a four-phase abdominal CT gives the same radiation dose as 300 chest X-rays. Several methods that can reduce

1525-700: Is imaging the contents of sarcophagi or ceramics. Recently, CWI in Amsterdam has collaborated with Rijksmuseum to investigate art object inside details in the framework called IntACT. Varied types of fungus can degrade wood to different degrees, one Belgium research group has been used X-ray CT 3 dimension with sub-micron resolution unveiled fungi can penetrate micropores of 0.6 μm under certain conditions. Sawmills use industrial CT scanners to detect round defects, for instance knots, to improve total value of timber productions. Most sawmills are planning to incorporate this robust detection tool to improve productivity in

1586-420: Is learned from training data using techniques from machine learning such as convolutional neural networks , while still incorporating the image formation model. This typically gives faster and higher quality reconstructions and has been applied to CT and MRI reconstruction. The advantages of the iterative approach include improved insensitivity to noise and capability of reconstructing an optimal image in

1647-461: Is limited technique as it displays only the surfaces that meet a particular threshold density, and which are towards the viewer. However, In volume rendering, transparency, colours and shading are used which makes it easy to present a volume in a single image. For example, Pelvic bones could be displayed as semi-transparent, so that, even viewing at an oblique angle one part of the image does not hide another. An important issue within radiology today

1708-607: Is often the preferred investigation modality for thyroid abnormalities. A CT scan can be used for detecting both acute and chronic changes in the lung parenchyma , the tissue of the lungs . It is particularly relevant here because normal two-dimensional X-rays do not show such defects. A variety of techniques are used, depending on the suspected abnormality. For evaluation of chronic interstitial processes such as emphysema , and fibrosis , thin sections with high spatial frequency reconstructions are used; often scans are performed both on inspiration and expiration. This special technique

1769-441: Is possible as present CT scanners provide almost isotropic resolution. MPR is used almost in every scan. The spine is frequently examined with it. An image of the spine in axial plane can only show one vertebral bone at a time and cannot show its relation with other vertebral bones. By reformatting the data in other planes, visualization of the relative position can be achieved in sagittal and coronal plane. New software allows

1830-402: Is possible to reconstruct images from data acquired in a very short time as required for real-time MRI (rt-MRI). In Cryo Electron Tomography , where the limited number of projections are acquired due to the hardware limitations and to avoid the biological specimen damage, it can be used along with compressive sensing techniques or regularization functions (e.g. Huber function ) to improve

1891-476: Is set by the operator (e.g., a level that corresponds to bone). With the help of edge detection image processing algorithms a 3D model can be constructed from the initial data and displayed on screen. Various thresholds can be used to get multiple models, each anatomical component such as muscle, bone and cartilage can be differentiated on the basis of different colours given to them. However, this mode of operation cannot show interior structures. Surface rendering

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1952-521: Is today the gold standard for diagnosing urinary stones . The size, volume and density of stones can be estimated to help clinicians guide further treatment; size is especially important in predicting spontaneous passage of a stone. For the axial skeleton and extremities , CT is often used to image complex fractures , especially ones around joints, because of its ability to reconstruct the area of interest in multiple planes. Fractures, ligamentous injuries, and dislocations can easily be recognized with

2013-573: Is when the original algorithm is "feasibility-seeking" (in the sense that it strives to find some point in a feasible region that is compatible with a family of constraints) and the perturbations that are introduced into the original iterative algorithm aim at reducing (not necessarily minimizing) a given merit function. In this case, superiorization has a unique place in optimization theory and practice. Many constrained optimization methods are based on methods for unconstrained optimization that are adapted to deal with constraints. Such is, for example,

2074-458: The brain , where CT perfusion imaging can often detect poor brain perfusion well before it is detected using a conventional spiral CT scan. This is better for stroke diagnosis than other CT types. Positron emission tomography–computed tomography is a hybrid CT modality which combines, in a single gantry, a positron emission tomography (PET) scanner and an X-ray computed tomography (CT) scanner, to acquire sequential images from both devices in

2135-411: The pulmonary arteries . CT scans can reduce the risk of angiography by providing clinicians with more information about the positioning and number of clots prior to the procedure. A CT scan of the heart is performed to gain knowledge about cardiac or coronary anatomy. Traditionally, cardiac CT scans are used to detect, diagnose, or follow up coronary artery disease . More recently CT has played

2196-423: The 1970s, CT has become an important tool in medical imaging to supplement conventional X-ray imaging and medical ultrasonography . It has more recently been used for preventive medicine or screening for disease, for example, CT colonography for people with a high risk of colon cancer , or full-motion heart scans for people with a high risk of heart disease. Several institutions offer full-body scans for

2257-432: The acquired data is an inverse problem . Often, it is not possible to exactly solve the inverse problem directly. In this case, a direct algorithm has to approximate the solution, which might cause visible reconstruction artifacts in the image. Iterative algorithms approach the correct solution using multiple iteration steps, which allows to obtain a better reconstruction at the cost of a higher computation time. There are

2318-408: The atomic number of the element used: Titanium usually has an amount of +1000 HU, iron steel can completely block the X-ray and is, therefore, responsible for well-known line-artifacts in computed tomograms. Artifacts are caused by abrupt transitions between low- and high-density materials, which results in data values that exceed the dynamic range of the processing electronics. CT data sets have

2379-505: The bends in a vessel, thereby helping to visualize a whole vessel in a single image or in multiple images. After a vessel has been "straightened", measurements such as cross-sectional area and length can be made. This is helpful in preoperative assessment of a surgical procedure. For 2D projections used in radiation therapy for quality assurance and planning of external beam radiotherapy , including digitally reconstructed radiographs, see Beam's eye view . A threshold value of radiodensity

2440-425: The case of incomplete data. The method has been applied in emission tomography modalities like SPECT and PET , where there is significant attenuation along ray paths and noise statistics are relatively poor. Statistical, likelihood-based approaches : Statistical, likelihood-based iterative expectation-maximization algorithms are now the preferred method of reconstruction. Such algorithms compute estimates of

2501-642: The class of projected gradient methods wherein the unconstrained minimization inner step "leads" the process and a projection onto the whole constraints set (the feasible region) is performed after each minimization step in order to regain feasibility. This projection onto the constraints set is in itself a non-trivial optimization problem and the need to solve it in every iteration hinders projected gradient methods and limits their efficacy to only feasible sets that are "simple to project onto". Barrier methods or penalty methods likewise are based on unconstrained optimization combined with various "add-on"s that guarantee that

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2562-446: The conservation and preservation of objects of cultural heritage. For many fragile objects, direct research and observation can be damaging and can degrade the object over time. Using CT scans, conservators and researchers are able to determine the material composition of the objects they are exploring, such as the position of ink along the layers of a scroll, without any additional harm. These scans have been optimal for research focused on

2623-485: The constraints are preserved. Regularization methods embed the constraints into a "regularized" objective function and proceed with unconstrained solution methods for the new regularized objective function. In contrast to these approaches, the superiorization methodology can be viewed as an antipodal way of thinking. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce merit function values. This

2684-452: The development of computer-assisted tomography". On the basis of image acquisition and procedures, various type of scanners are available in the market. Sequential CT, also known as step-and-shoot CT, is a type of scanning method in which the CT table moves stepwise. The table increments to a particular location and then stops which is followed by the X-ray tube rotation and acquisition of

2745-472: The general population although this practice goes against the advice and official position of many professional organizations in the field primarily due to the radiation dose applied. The use of CT scans has increased dramatically over the last two decades in many countries. An estimated 72 million scans were performed in the United States in 2007 and more than 80 million in 2015. CT scanning of

2806-579: The head is also used in CT- guided stereotactic surgery and radiosurgery for treatment of intracranial tumors, arteriovenous malformations , and other surgically treatable conditions using a device known as the N-localizer . Contrast CT is generally the initial study of choice for neck masses in adults. CT of the thyroid plays an important role in the evaluation of thyroid cancer . CT scan often incidentally finds thyroid abnormalities, and so

2867-453: The head is typically used to detect infarction ( stroke ), tumors , calcifications , haemorrhage , and bone trauma . Of the above, hypodense (dark) structures can indicate edema and infarction, hyperdense (bright) structures indicate calcifications and haemorrhage and bone trauma can be seen as disjunction in bone windows. Tumors can be detected by the swelling and anatomical distortion they cause, or by surrounding edema. CT scanning of

2928-450: The higher cost associated with building a much larger X-ray tube and detector array and limited anatomical coverage. Dual Energy CT, also known as Spectral CT, is an advancement of Computed Tomography in which two energies are used to create two sets of data. A Dual Energy CT may employ Dual source, Single source with dual detector layer, Single source with energy switching methods to get two different sets of data. CT perfusion imaging

2989-527: The insides of these objects, as was the case with the virtual unwrapping of the En-Gedi scroll and the Herculaneum papyri . Micro-CT has also proved useful for analyzing more recent artifacts such as still-sealed historic correspondence that employed the technique of letterlocking (complex folding and cuts) that provided a "tamper-evident locking mechanism". Further examples of use cases in archaeology

3050-487: The key uses for CT scanning have been flaw detection, failure analysis, metrology, assembly analysis, image-based finite element methods and reverse engineering applications. CT scanning is also employed in the imaging and conservation of museum artifacts. CT scanning has also found an application in transport security (predominantly airport security ) where it is currently used in a materials analysis context for explosives detection CTX (explosive-detection device) and

3111-694: The likely distribution of annihilation events that led to the measured data, based on statistical principle, often providing better noise profiles and resistance to the streak artifacts common with FBP. Since the density of radioactive tracer is a function in a function space, therefore of extremely high-dimensions, methods which regularize the maximum-likelihood solution turning it towards penalized or maximum a-posteriori methods can have significant advantages for low counts. Examples such as Ulf Grenander 's Sieve estimator or Bayes penalty methods, or via I.J. Good 's roughness method may yield superior performance to expectation-maximization-based methods which involve

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3172-441: The long run, however initial investment cost is high. The result of a CT scan is a volume of voxels , which may be presented to a human observer by various methods, which broadly fit into the following categories: Technically, all volume renderings become projections when viewed on a 2-dimensional display , making the distinction between projections and volume renderings a bit vague. The epitomes of volume rendering models feature

3233-416: The projection data. In Magnetic Resonance Imaging it can be used to reconstruct images from data acquired with multiple receive coils and with sampling patterns different from the conventional Cartesian grid and allows the use of improved regularization techniques (e.g. total variation ) or an extended modeling of physical processes to improve the reconstruction. For example, with iterative algorithms it

3294-587: The recommended guidelines, in an attempt to do surveillance on the nodules. However, established guidelines advise that patients without a prior history of cancer and whose solid nodules have not grown over a two-year period are unlikely to have any malignant cancer. For this reason, and because no research provides supporting evidence that intensive surveillance gives better outcomes, and because of risks associated with having CT scans, patients should not receive CT screening in excess of those recommended by established guidelines. Computed tomography angiography (CTA)

3355-495: The reconstruction for better interpretation. Here is an example that illustrates the benefits of iterative image reconstruction for cardiac MRI. Computed tomography A computed tomography scan ( CT scan ), formerly called computed axial tomography scan ( CAT scan ), is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers or radiology technologists. CT scanners use

3416-450: The reconstruction of data in non-orthogonal (oblique) planes, which help in the visualization of organs which are not in orthogonal planes. It is better suited for visualization of the anatomical structure of the bronchi as they do not lie orthogonal to the direction of the scan. Curved-plane reconstruction (or curved planar reformation = CPR) is performed mainly for the evaluation of vessels. This type of reconstruction helps to straighten

3477-479: The same session, which are combined into a single superposed ( co-registered ) image. Thus, functional imaging obtained by PET, which depicts the spatial distribution of metabolic or biochemical activity in the body can be more precisely aligned or correlated with anatomic imaging obtained by CT scanning. PET-CT gives both anatomical and functional details of an organ under examination and is helpful in detecting different type of cancers. Since its introduction in

3538-422: The use of thin sections and physical preparation. X-ray CT is used in paleontology to non-destructively visualize fossils in 3D. This has many advantages. For example, we can look at fragile structures that might never otherwise be able to be studied. In addition, one can freely move around models of fossils in virtual 3D space to inspect it without damaging the fossil. X-ray CT and micro-CT can also be used for

3599-459: The view that physicians generally have in reality when positioned in front of patients. Pixels in an image obtained by CT scanning are displayed in terms of relative radiodensity . The pixel itself is displayed according to the mean attenuation of the tissue(s) that it corresponds to on a scale from +3,071 (most attenuating) to −1,024 (least attenuating) on the Hounsfield scale . A pixel

3660-529: The window are displayed as a gray intensity proportional to position within the window. The window used for display must be matched to the X-ray density of the object of interest, in order to optimize the visible detail. Window width and window level parameters are used to control the windowing of a scan. Multiplanar reconstruction (MPR) is the process of converting data from one anatomical plane (usually transverse ) to other planes. It can be used for thin slices as well as projections. Multiplanar reconstruction

3721-566: The workings of the Antikythera mechanism or the text hidden inside the charred outer layers of the En-Gedi Scroll . However, they are not optimal for every object subject to these kinds of research questions, as there are certain artifacts like the Herculaneum papyri in which the material composition has very little variation along the inside of the object. After scanning these objects, computational methods can be employed to examine

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