Bell state - Revision history

en>JamesCowley: Removed "vague" marker at end of introduction after explaining practical applications (or lack thereof) of FTL quantum mechanics

2014-11-24T15:11:18Z

Removed "vague" marker at end of introduction after explaining practical applications (or lack thereof) of FTL quantum mechanics

← Older revision		Revision as of 17:11, 24 November 2014
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	~~{{Refimprove\|date=July 2007}}~~		Another day I woke up and [http://www.senatorwonderling.com tickets to luke bryan concert] realised - At the moment I've been solitary for a little while and following much bullying from pals I now locate myself opted for web dating. They assured me that there are plenty of fun, pleasant and ordinary visitors to fulfill, so here goes the toss!<br>My family and buddies are awesome and hanging out with them at pub gigs or dinners is always a necessity. As I locate you could not have a nice dialogue [http://lukebryantickets.pyhgy.com luke bryan vip packages] using the sound I have never been in to night clubs. I also got 2 unquestionably cheeky and quite cute puppies who are always eager to meet fresh people.<br>I try to maintain as physically healthy as potential coming to the gym several times weekly. I love my athletics and endeavor to perform or watch as several a potential. Being [http://lukebryantickets.neodga.com cheapest luke bryan tickets] wintertime I shall regularly at Hawthorn fits. Note: I have observed the carnage of fumbling fits at stocktake sales, In case that you would [http://Www.Dailymail.Co.uk/home/search.html?sel=site&searchPhrase=considered+shopping considered shopping] an activity I do not brain.<br><br><br><br>Feel free to luke bryan show [[http://www.banburycrossonline.com http://www.banburycrossonline.com]] visit my web blog luke bryan tickets dallas ([http://lukebryantickets.flicense.com the full details])

	[~~[File~~:~~FBP Iter single~~.~~jpg\|thumb\|Example showing differences between filtered backprojection (right half) and iterative reconstruction method (left half)~~]]
	'~~''Iterative reconstruction''' refers to [[Iteration\|iterative]] [[algorithms]] used to reconstruct 2D~~ and ~~3D images in certain [[Digital imaging\|imaging]] techniques.~~
	~~For example, in [[computed tomography]] an image must be reconstructed~~ from ~~projections of an object~~. ~~Here, iterative reconstruction techniques~~ are 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.~~<~~ref name="ref1"~~>~~Herman, G. T., Fundamentals of computerized tomography: Image reconstruction from projection, 2nd edition, Springer, 2009</ref>~~

	~~== Basic concepts ==~~

	~~The reconstruction of an image from 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~~ [~~[Digital artifact\|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~~.

	~~In [[computed tomography~~]~~], this approach was~~ the ~~one first used by [[Godfrey Hounsfield\|Hounsfield]]~~. There are 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.~~

	~~There~~ are ~~typically five components~~ to ~~iterative image reconstruction algorithms,~~
	~~e.g.~~
	.<~~ref name="pwl"~~>
	~~J A Fessler, "Penalized weighted least-squares image reconstruction for positron emission tomography,"~~
	~~IEEE Trans. on Medical Imaging, 13(2):290-300, June 1994.~~
	~~</ref>~~
	~~# An object model that expresses the unknown continuous-space function <math>f(r)</math> that is~~ to ~~be reconstructed in terms of a finite series with unknown coefficients that must be estimated from~~ the ~~data~~.
	~~# A system model that relates the unknown object~~ to ~~the "ideal" measurements that would be recorded in the absence of measurement noise. Often this is~~ a ~~linear model of the form <math>\mathbf{A}x</math>~~.
	~~# A~~ [~~[statistical model]] that describes how the noisy measurements vary around their ideal values~~. ~~Often [[Gaussian noise]] or [[Poisson statistics]] are assumed~~.
	~~# A [[Loss function\|cost function~~]~~] that is to be minimized to estimate the image coefficient vector~~. ~~Often this cost function includes some form of [[regularization]]. Sometimes the regularization is based on [[Markov random fields]].~~
	~~# An [[algorithm]], usually iterative, for minimizing the cost function, including some initial estimate of the image and some stopping criterion for terminating~~ the ~~iterations.~~

	~~== Advantages ==~~

	~~The advantages~~ of the iterative approach include improved insensitivity to [[signal noise\|noise]] and capability of reconstructing an [[Optimization (mathematics)\|optimal]] image in the case of incomplete data. The method has been applied in emission tomography modalities like [[SPECT]] and [[Positron emission tomography\|PET]], where there is significant attenuation along ray paths and [[noise statistics]] are relatively poor.

	~~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 [[artifact (observational)\|artifacts]]~~
	~~<ref name="mdt">~~
	~~FE Boas and D Fleischmann. "~~[http://~~radiology~~.~~rsna.org/content/early/2011/02/17/radiol~~.~~11101782~~.~~abstract Evaluation of two iterative techniques for reducing metal artifacts in computed tomography.]" Radiology, {{doi\|10.1148~~/~~radiol.11101782}}, 2011.~~
	</~~ref>~~
	~~require the exclusion of some portions of 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<ref>Pruessmann, K. P~~.~~, Weiger, M., Börnert, P. and Boesiger, P. (2001), Advances in sensitivity encoding with arbitrary k-space trajectories. Magnetic Resonance in Medicine, 46: 638–651. {{doi\|10.1002/mrm.1241}}~~<~~/ref~~> ~~and allows the use of improved regularization techniques (e.g. [[total variation]])~~<~~ref~~>Block, K. T., Uecker, M. and Frahm, J. (2007), Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint. Magnetic Resonance in Medicine, 57: 1086–1098. {{doi\|10.1002/mrm.21236}}<~~/ref~~> ~~or an extended modeling of physical processes~~<~~ref>Fessler, J. (2010) Model-based Image Reconstruction for MRI. Signal Processing Magazine, IEEE 27:81-89</ref~~> to ~~improve the reconstruction. For example, with iterative algorithms it is possible to~~
	~~reconstruct images from data acquired in a very short time as required for~~ [[~~Real-time MRI]].<ref name=uecker2010>M Uecker, S Zhang, D Voit, A Karaus, KD Merboldt, J Frahm (2010a) Real-time MRI at a resolution of 20 ms. NMR Biomed 23~~: ~~986-994, {{doi\|10.1002~~/~~nbm.1585}}<~~/~~ref>~~

	~~Here is an example that illustrates the benefits of iterative image reconstruction for cardiac MRI~~.~~<ref name="ilyas Uyanik 2013">I Uyanik, P Lindner, D Shah, N Tsekos I Pavlidis (2013) Applying a Level Set Method for Resolving Physiologic Motions in Free-Breathing and Non-gated Cardiac MRI~~. ~~FIMH, 2013, [~~http://www.~~cpl~~.~~uh.edu/files/publications/conf_paper_videos/c66.pdf~~]~~</ref>~~

	[~~[File~~:~~Heart-direct-vs-iterative-reconstruction~~.~~png\|frame\|A single frame from a [[Real-time MRI]] movie of a [[human heart]]~~. ~~a) direct reconstruction b) iterative (nonlinear inverse) reconstruction<ref name=uecker2010 />]]~~

	~~==See also==~~

	*[[Tomographic reconstruction]]
	*[[Tomogram]]
	*[[Computed Tomography]]
	*[[Magnetic Resonance Imaging]]
	*[[Inverse problem]]
	*[[Osem (mathematics)~~\|Osem]]~~
	*[[Deconvolution]]

	~~==References==~~
	~~<references/>~~

	~~{{commons category\|Iterative reconstruction}}~~

	~~{{DEFAULTSORT:Iterative Reconstruction}}~~
	~~[[Category:Medical imaging]]~~

en>MindReader 1984 at 01:45, 1 February 2014

2014-02-01T01:45:36Z

← Older revision		Revision as of 03:45, 1 February 2014
Line 1:		Line 1:
	~~Last week I woke up~~ and ~~realized - Now I have been solitary for a while~~ and ~~after much intimidation~~ from ~~friends I today locate myself registered for web dating~~. ~~They guaranteed me that there~~ are ~~plenty of enjoyable~~, ~~sweet and normal people~~ to ~~meet~~, ~~so here goes~~ the ~~message!~~<br>~~I endeavor to maintain as toned as possible [http~~:/~~/lukebryantickets~~.~~sgs-suparco~~.~~org luke bryan concert dates~~] ~~being~~ at the ~~gymnasium several times weekly~~. ~~I appreciate my athletics~~ and ~~try~~ to ~~perform or watch because many a possible~~. ~~I shall regularly at Hawthorn [http~~://~~www~~.~~ffpjp24~~.~~org buy luke bryan tickets~~] ~~suits being winter~~. ~~Notice: I've observed~~ the ~~carnage~~ of ~~fumbling matches at stocktake sales~~, ~~Supposing that you would~~ considered ~~purchasing an activity I don't brain~~.<br>~~My pals~~ and ~~family are wonderful and spending some time together at~~ [http://~~www~~.~~netpaw~~.org ~~luke bryan sold out~~] ~~tavern gigs or meals is definitely vital~~. ~~I have never been into dance clubs as I realize you could not get a significant dialog together~~ with the ~~sound~~. ~~Additionally~~, ~~I got two definitely cheeky~~ and ~~[http~~://~~www~~.~~cinemaudiosociety~~.~~org luke bryan on sale dates~~] ~~very cunning puppies that are constantly eager to meet up fresh individuals~~.<br><br>~~Feel free~~ to ~~surf~~ to ~~my homepage~~: [http://www.~~dailymail~~.co.uk/~~home~~/~~search~~.~~html?sel~~=~~site&searchPhrase~~=~~luke+bryan luke bryan~~] ~~concert dates~~ ([~~http~~:~~//lukebryantickets.hamedanshahr.com Recommended Browsing~~])		{{Refimprove\|date=July 2007}}

			[[File:FBP Iter single.jpg\|thumb\|Example showing differences between filtered backprojection (right half) and iterative reconstruction method (left half)]]
			'''Iterative reconstruction''' refers to [[Iteration\|iterative]] [[algorithms]] used to reconstruct 2D and 3D images in certain [[Digital imaging\|imaging]] techniques.
			For example, in [[computed tomography]] an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are 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.<ref name="ref1">Herman, G. T., Fundamentals of computerized tomography: Image reconstruction from projection, 2nd edition, Springer, 2009</ref>

			== Basic concepts ==

			The reconstruction of an image from 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 [[Digital artifact\|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.

			In [[computed tomography]], this approach was the one first used by [[Godfrey Hounsfield\|Hounsfield]]. There are 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.

			There are typically five components to iterative image reconstruction algorithms,
			e.g.
			.<ref name="pwl">
			J A Fessler, "Penalized weighted least-squares image reconstruction for positron emission tomography,"
			IEEE Trans. on Medical Imaging, 13(2):290-300, June 1994.
			</ref>
			# An object model that expresses the unknown continuous-space function <math>f(r)</math> that is to be reconstructed in terms of a finite series with unknown coefficients that must be estimated from the data.
			# A system model that relates the unknown object to the "ideal" measurements that would be recorded in the absence of measurement noise. Often this is a linear model of the form <math>\mathbf{A}x</math>.
			# A [[statistical model]] that describes how the noisy measurements vary around their ideal values. Often [[Gaussian noise]] or [[Poisson statistics]] are assumed.
			# A [[Loss function\|cost function]] that is to be minimized to estimate the image coefficient vector. Often this cost function includes some form of [[regularization]]. Sometimes the regularization is based on [[Markov random fields]].
			# An [[algorithm]], usually iterative, for minimizing the cost function, including some initial estimate of the image and some stopping criterion for terminating the iterations.

			== Advantages ==

			The advantages of the iterative approach include improved insensitivity to [[signal noise\|noise]] and capability of reconstructing an [[Optimization (mathematics)\|optimal]] image in the case of incomplete data. The method has been applied in emission tomography modalities like [[SPECT]] and [[Positron emission tomography\|PET]], where there is significant attenuation along ray paths and [[noise statistics]] are relatively poor.

			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 [[artifact (observational)\|artifacts]]
			<ref name="mdt">
			FE Boas and D Fleischmann. "[http://radiology.rsna.org/content/early/2011/02/17/radiol.11101782.abstract Evaluation of two iterative techniques for reducing metal artifacts in computed tomography.]" Radiology, {{doi\|10.1148/radiol.11101782}}, 2011.
			</ref>
			require the exclusion of some portions of 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<ref>Pruessmann, K. P., Weiger, M., Börnert, P. and Boesiger, P. (2001), Advances in sensitivity encoding with arbitrary k-space trajectories. Magnetic Resonance in Medicine, 46: 638–651. {{doi\|10.1002/mrm.1241}}</ref> and allows the use of improved regularization techniques (e.g. [[total variation]])<ref>Block, K. T., Uecker, M. and Frahm, J. (2007), Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint. Magnetic Resonance in Medicine, 57: 1086–1098. {{doi\|10.1002/mrm.21236}}</ref> or an extended modeling of physical processes<ref>Fessler, J. (2010) Model-based Image Reconstruction for MRI. Signal Processing Magazine, IEEE 27:81-89</ref> to improve the reconstruction. For example, with iterative algorithms it is possible to
			reconstruct images from data acquired in a very short time as required for [[Real-time MRI]].<ref name=uecker2010>M Uecker, S Zhang, D Voit, A Karaus, KD Merboldt, J Frahm (2010a) Real-time MRI at a resolution of 20 ms. NMR Biomed 23: 986-994, {{doi\|10.1002/nbm.1585}}</ref>

			Here is an example that illustrates the benefits of iterative image reconstruction for cardiac MRI.<ref name="ilyas Uyanik 2013">I Uyanik, P Lindner, D Shah, N Tsekos I Pavlidis (2013) Applying a Level Set Method for Resolving Physiologic Motions in Free-Breathing and Non-gated Cardiac MRI. FIMH, 2013, [http://www.cpl.uh.edu/files/publications/conf_paper_videos/c66.pdf]</ref>

			[[File:Heart-direct-vs-iterative-reconstruction.png\|frame\|A single frame from a [[Real-time MRI]] movie of a [[human heart]]. a) direct reconstruction b) iterative (nonlinear inverse) reconstruction<ref name=uecker2010 />]]

			==See also==

			*[[Tomographic reconstruction]]
			*[[Tomogram]]
			*[[Computed Tomography]]
			*[[Magnetic Resonance Imaging]]
			*[[Inverse problem]]
			*[[Osem (mathematics)\|Osem]]
			*[[Deconvolution]]

			==References==
			<references/>

			{{commons category\|Iterative reconstruction}}

			{{DEFAULTSORT:Iterative Reconstruction}}
			[[Category:Medical imaging]]

42.241.29.162: Disambiguated: hidden variable → hidden variable theory, basis → basis (linear algebra)

2012-05-26T04:44:46Z

Disambiguated: hidden variable → hidden variable theory, basis → basis (linear algebra)

New page

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