Merken
High resolution Magnetic Resonance Imaging experiments  lessons in nonlinear statistical modeling
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Erkannte Entitäten
Sprachtranskript
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the so will have the only what I want to do speak about a sort of a poem in that book the because
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in the context of follow in view of all then histology so in the hood vendors storage Quetelet topic
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in a new sense in a moment and the it aims for I a became microscopic shown of once to a diverse population variability you're in the mall studies in the subject anatomical differences so of aims for investigation of rare diseases and 1 of the central issues here this Compaq their compatibility between studies of done wonderful and scanners inside it's all already at different types and though already so the techniques used here and they require are leave high image resolution in order will of get to the point of and the West auditory in diffusion along that will explain it to live and work in in detail after world so we need might but I'd be very use which should be forced to work decrease sort of for the signal in the action and for 2 value is and above all these things they have the consequences but in the so we have problems of status he could poverty his of on data we have Valiant Lewis and all of this causes consequences for statistical modeling especially if you use nonunion moderates and the intuitive it would use bias due to variability so there will be 2 were modalities Scylla look at once diffusion along to the 2nd 1 is my department at being called pointing to in whole OK let's have a look at that that
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position President in them what you measure all of relaxations so in kspace and so so in signal this complex Coliseum we have multiple receive a chorus of of and the signal that you get from each corner that's transformed using fast Fourier transform of into with image space so what you see you soon image still what you see is image like this this has the funny going intensity depending go on now the positioning the receiver coil but in order to would get 1 image so you take the images from the different receiver cards in complex spaces and you combine them using some liable in down so the model for the quality the most common is probably gap not all mismatch a good click amended 1 in the form of a perspective would be sense and the what it makes us it goes from a complex Gaussian or transforms the sigma distribution from a complex goes here in of all from a high C in magnitude image toward the seat and distribution that's Monsanto CSI of the finance and keep down of the corresponding pool scared cygnus scared by the most end the soap number of degrees of freedom and this so the number of degrees of freedom depends on the construction I was so and cancer the case of sense it's 1 this cop on it of depends on the location and on the size of the coil sensitivities and so on subsampling kernel that is applied so so it can be of that he adds varying curve of location as 1 of also segments link looking the frication on the other the signal the solution of
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this months and excite of the signal that we are interested in isn't consonants and pretty problem at that we have depend on location depending on that issue on depending corn not look at anatomy the expected signal hasn't complicated form and the central point here is that the expected expected signal then the Davidic is seeking and we also have a certain variants loaded again depend on the parameters of the
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distribution so whole does it of the problem looked like depending go on of the signal to noise of IF signal to noise this let's say of 1 day and night we have a gap and what is sigma sealed we have a gap between the circulating give a U. N followed their of the expected value that's so required lounge if further the signal for wanders so get now wars and close for signals are larger than 4 in principle you can start neglecting cover the difference but our absolute discovered the disk upon his policy depending on signal to noise this what you see all over OK on this link that of host modality diffusion weighted imaging he addition to world those scheme applied in all a tool in get to on match in addition the diffusion again at the end of this election supplied and this diffusion gradient though this causes the particulates to world diffuse in the direction of the gradient then at some point good idea and this sort of advanced so it starts coming back and what so and into the snow is in the probability density of describing because the of the poppy because of poverty disease the of particle it's slow to have from 1 position to another position in time tall only this information is usually out in the that's all of our volume elements or voxels so what you get from the denial of oxygen and took over a certain distance of clever and of this depends of course of in emissions the density of particles looking
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at this is done this flow quite a model of different that actions on this view and different staying softer of 2 gradient difference planes could of course 1 into the what you do you again and so on you this kind of on the door all the signal attenuation so that means the loss of signal is a quotient of the security of soft applying to the diffusion gradient and the signal that you walk self the fault such a good idea and you measure as for that say between Leslie and Tong and different elections for them off for Canadians Steitz can't all
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he at what it did all of this this yeah in which show of 4 on with all the good is that the futility and and if you increase the of diffusion gradient so that cigna gets lower and lower and the the signal to noise ratio of decreases and of on the same scale you
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see that effect so here in this in these images so much on all skip and a maximum so you have much that much less signal to noise ratio what we
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for we have been looking at so human conic Thom they and and that's so the amount of data the best this quantity that the way will and from it's the concept of science once work but we know the degrees of freedom for the addition of solution which is to and what you see here if you were analyze images from difference the which its it is slowed at the of the 90 percent still of boxes in an image that was acquired before the value of sleep wasn't of work as a signal to noise visual of list and for what and though even the flow the very 1 thousand Mr. so the person so we have a situation where most of the images that has seen me bias of in the day there you are it's an expected signal is much larger than the Teletalk a signal that we all usually using in modeling what he this is for an image data it comes all at all from the image reconstruction what is stand all usually is
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so some people sink and preprocessing girl here consists of follow collections form a new the feared effects such as the stability of the distortion Collins also collection fullmotion effects because the different images they are quiet the in sequentially in time and the some yes to all of aligning the different the images him of this all these collections on principle of interpolations but we in our neighbor link boxes these interpolations the total reduction variants but you don't change showed of those of the expected signal so the biases of the images that you get look much less noisy but the bias is so much affected that senescence customers units in order to bless this ability of the problem so it is you have to catalyze of cygnus enormous all characterize the bias using many many processed data commingled of the image the construction and not this use the done plus stable of what
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the so what in diffusion that at the time that's the description of followed what experiment is set up for on the the human connectome portrait what you have speed times 90 canadians slowly of uniform need distributed all on this fiercely values and the classical model used in analysis You're this the diffusion kinds models so you describe though water this fusion as findings a poll peak Gaussian diffusion this leads to a situation where you have a basic and ends a key debts and principled its seal will you and you have a description by of speed times the tens of and this can then be used in order to of care that the highest so the anisotropy influenced by comic ordered if any MEPs to hear collar of cosponsored election intensity corresponds to what but this it'll p on those elites tool main directions of diffusion which can be but used order to work on stock price hikes OK no
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it's usually done this he in the situation of that money out aggression this applied so what 1 of our compares the OPS soft signal this go to medical signal it would take a signal based on the model depending on problem us so in principle the 1 assumes 1 has an additive Gaussian model I was from 4 expectancy page that expectancy will end though the resultant certain areas and the what this does is so it doesn't X to the of estimate of the parameter of interest for but the FIL plage protection Palomita so the parameter that this estimate that this still porch action that's in the flame bark off for know the the assumed linearly aggression 1 Eitel notice but collect iterative would be to use something like closet like note closet like the look like you because so after preprocessing cree don't have control of the 1 in the the signal distribution anymore but what we know this this expected value of the signal is though expect that there can be described as a function of utility convey you and nice so this this estimates parameters in and I had a cop modern buying weighted least this OK if
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you look at as in politics on some legal melody conditions on the model that OSF it you what you get is for the money nearly Gaussian model you get done asymptotic distribution for the difference of the estimated parameters in the projection pattern we don't of the phis Valiant and expect the expectations he or for clause let you would you get an asymptotic gaussian distribution of sent out so the pool parameter or talk of don't little slightly different covariance with the OK let's have what are the consequences here but due to inadequate modeling you have a bias that flow this'll flecked that's by the Dutch ovens so of the projection but and the at it does not ban of issue with increasing sample sites but on our side there's also bias due to variability then nonlinear of this can be accessed using credited approximation and what you get all the fit the slower bias which depends on the slope of and in a approximation and all you know the metrics w we'll get to you have thought in the quadratic town and this bait bias from 1 what was sigma square up here despite his managers this so besides Gaussian finicky and the on 1 side all if the signal goes to see and there are metal it's in order to we use forms spatial information in order to the reduce the variability you and was it depends on the curvature all of the regression model if he it's essential that the curvature after regression model consists of component the other 1 is includes a the cover that can't be awarded the number 1 this so parameter induced curvature empowerment and use color charge is something that you have influence on using you could colic parameterization here is essential OK how we have done some
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simulations based on notice of input good of Our findings and those using to design from the Yuma ComicCon project and the we use the has a problematization ya of which makes them as input the code goes in distribution more reliable some approximation and it's you think of life was describing depends on in a little expects so for the many of the computer that I had no followers duplicate you at of and so we very know signal to noise and we value you go function and as a and so what you have you this so the bias that you get for values use of toward f any on with their estimates estimated the prediction permitted that you get for the use of 2 1 essay from C 0 comma decimal 1 to seal comma decimal 9 end at different values of sigma corresponding to different the use of force to signaltonoise question but what he's so what you see you have you stood biased due to 1 model misspecification
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the from the summation study what you get all of this so the combination of bias for our modest misspecification bias from variability and what you see here as so all of those and black that's so it wasn't like you would the estimates of as the function and as a little peak and what you see in our the plant is slow the side that you get by Monday nearly Lushan using that for small if any the there are is a bias and was elected with close the comes from very avidity the overhaul bias of regression estimator this sort compatibility the small which is due to of the concert encode the consonant effect between the 2 variables types of finances good if you have a median where the use of a larger values of of the difference between them both middle it's it's significant people booking saying if you look at this eigen values with you know you have done FIL and let the 1st and that is the 2nd and in getting the support I mean value of R. down I or of on use break was it that you want and that's a cost when sites by Monday nearly Gaussian OK what you of
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looking at close to human comment on that on the finding goes that goes out if you look at the difference between Posilac you wouldn't the least mass estimates but we see that there's if any difference of a ball to I C 0 point all toward most for quantity the glyphs between 0 and 1 and this mode performance is pitch should depend so it's especially large in white matter and us and you see the same effect that if you look at I think
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it's of this investigated the Buddha's ability of this the sites looking not on 1 subject but 1 100 subjects and those looking at mean of any for 2 legions 1 is corpus come was on and the 1 that the 2nd 1 astronomers coppers on this sort of the Legion you know the tens of this so I think what the you have in and was so you have a much lower the value of free of which only corresponds to world what of variation defined the structure and what you see see in each case you have a shift in of the estimated values of a boat seal opens here 5 which Syria and so of some money and he's grass consistently underestimates estimates that any in boasts legions by some value if if you move to a different scanner the difference would be something different a somewhat different that you would expect that closet of an electorate exceed estimates are much cooler to check the chart and than on the Gaussian estimates what he had
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Malaysia please song the 2nd modality quantitative atomic imaging going on so what you do
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use measure sequences of for different parameters and different continents and to
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combine them by a model and but
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again yes nonlinear model
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that so depends on the set of a set of of dance and you are interested in dynamiclink maps that cut the sum all colocalized tissue and death here for
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this they've done when a situation that for our in we don't really know what so the degrees of freedom song but due to the to the construction adult and the see that there's so of the bias that flow depends on the tissue type so yeah that the active by slow that active systematic this reasonably small if we
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analyze the 4 different value of his style the number of degrees of freedom this 1 this much more Mr. Shor public construction but would you see you have an I want it goes up to 50 per cent in the estimate of
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what we but again that's of
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specific what conclusions image reconstruction and flow combination of singer Cohen images from power of acquisitions dataminded sigma distributions of we know that the US government of developed methods for adaptive estimation of of signal and also for production in of noise in using special information which always tool use clumsy like you would end and also the lowest to work at the less so the liability issue combination of complex images as incense should be put forward in order to work know what the number of degrees of freedom crossing acute should be used to the we have to analyze me many data in order to work the highest the bias of we book and of the other ones and let me at the end just
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mentioned of the or collaborators so would this work
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if clues scores the stand to together with constant and general diamonds will
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of B and so get had to ask the Program ink and so the next fall all physicists slow reuse Copal grateful move referring to very gets poems from last what order so if specialist in our local medics what
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the just some differences in
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preference for you to software developed in all look at things that were
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much kind of the
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of of the of the of the of the of the
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Metadaten
Formale Metadaten
Titel  High resolution Magnetic Resonance Imaging experiments  lessons in nonlinear statistical modeling 
Serientitel  The Leibniz "Mathematical Modeling and Simulation" (MMS) Days 2018 
Autor 
Polzehl, Jörg

Mitwirkende 
LeibnizInstitut für Oberflächenmodifizierung e.V. (IOP)

Lizenz 
CCNamensnennung 3.0 Deutschland: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. 
DOI  10.5446/35350 
Herausgeber  WeierstraßInstitut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) 
Erscheinungsjahr  2018 
Sprache  Englisch 
Produktionsort  Leipzig 
Inhaltliche Metadaten
Fachgebiet  Informatik, Mathematik 
Abstract  Recent advances in neuroimaging attempt to enable invivo histology of the brain. Doing so requires increased spatial resolution up to a situation where the signal meets the noise floor. The talk will cover research conducted at WIAS, in collaboration with MR physicists, on statistical issues in modeling imaging data characterized by low signaltonoise ratio (SNR). I'll cover several specific, but interrelated problems:  characterization of the signal distribution in MR experiments,  effects of preprocessing on the signal distribution,  estimation of the noise profile in MR images,  use of spatial information for variance reduction in (collections of) MR images,  bias due to incorrect modeling in MR experiments. I'll consider two specific imaging experiments to illustrate problems, characterize effects that are due to high measurment noise and provide solutions for:  diffusion weighted MR, with an analysis based on data of the Human Connectome Project,  multiparameter mapping, using data measured at the Wellcome Trust Center for Neuroimaging, London. Literature: S. Becker, K. Tabelow, S. Mohammadi, N. Weiskopf and J. Polzehl, Adaptive smoothing of multishell diffusionweighted MR data by msPOAS, NeuroImage, 95 (2014) pp. 90105. K. Tabelow, H.U. Voss and J. Polzehl, Local estimation of the noise level in MRI using structural adaptation, Medical Image Analysis, 20 (2015) pp. 7686. J. Polzehl and K. Tabelow, Low SNR in dMRI models, JASA, 11 (2016) pp. 14801490. K. Tabelow, Ch. D'Alonzo, L. Ruthotto, M. F. Callaghan, N. Weiskopf, J. Polzehl and S. Mohammadi, Removing the estimation bias due to the noise floor in multiparameter maps, ISMRM annual meeting 2017. 