Welcome back everybody to Beyond the Patterns. Today we have another invited presentation

and today I want to introduce Jinwei Zhang, who is a PhD student at Cornell MRI Research

Lab under the supervision of Jing Wang. The current focus of his work is to develop AI-based

methods to optimize the sampling and reconstruction process of MRI and especially quantitative

susceptibility mapping with multi-echo image acquisition and reconstruction.

Prior to Cornell he obtained a Bachelor of Science in Physics from Sun Yat-sen University.

So it's a great pleasure to have Jinwei here and his presentation is entitled Probabilistic

Dipole Inversion for Adaptive Quantitative Susceptibility Mapping and without further

ado, I'm very happy to announce Jinwei and the stage as yours.

Thank you Professor Miao, thank you for the introduction. Hi everyone, today I'm going

to show our work using probabilistic approach to solve the dipole inversion inverse problem

in quantitative susceptibility mapping. So the inverse problem we are solving here is

called quantitative susceptibility mapping, QSM. So QSM tries to solve the tissue susceptibility

chi from the magnetic field B and it's a spatial decomposition process with the dipole

kernel Loracus D and also with some measurement noise N. So if you look at an image space

it's a spatial decomposition process with the spatial dipole kernel and if you transform

this dipole kernel in k-space you will see this zero-coin surface in k-space. So because

of zero-coin, when you do this division in k-space that will cause some earplugs in the

QSM dipole inversion problem. So here this one is a typical local field and this is the

QSM we solve from this local field. So QSM is a developed contrast in the MRI that can

quantify some of the biomarkers in the tissue such as iron, calcium and gadolinium. So we

will see some of the applications of QSM in clinical diagnosis. So this is the QSM inverse

problem we are solving here. And there are some prior works in our lab that solve this

dipole inversion numerous problem in QSM. So for first approach is called Cosmos. So since

we know that there is a zero-coin in k-space of the dipole kernel, so we try to eliminate

this zero-coin by using multiple orientation scans. Because if we only use one scan we

will have this zero-coin. But if we rotate the main negative field by a certain angle,

such as for example if we scan three times using three different main negative field

direction, we can just cancel out this zero-coin. So this will make the earplugs inverse problem

in QSM well posed. So this is called Cosmos. So Cosmos has been the golden standard QSM

for both the algorithm development and clinical papers. But the drawback of Cosmos is very

obvious. It requires multiple orientation scan, which is not that feasible for clinical

verification. So another approach, more feasible approach, is called METI. So this is a single

orientation scan. So in single orientation we always have this zero-coin, which costs

the earplugs in QSM. So in order to tackle this earplugs, some prior or validation term

is needed. So here we use this structure information. So this is called binary value of the routine

matrix on the three spatial dimensions. So here we impose this to the variation of the

relation to surprise the artifact introduced by the zero-coin outside the tissue brain.

So this M is the mask outside the tissue brain. Then we solve this optimization problem using

iterative construction solver, such as conjugate brain descent, ADMM, or primal dual. So METI,

I think is a pioneer work using the regularized construction to solve QSM inverse problem.

And since METI, there are a lot of other works following this prior work, either changing

the relation term or using some other advanced solver or even deep learning-based solver.

So this is Cosmos METI. So the motivation of this work is that given the prior distribution

of stability and also the likelihood distribution, can we solve the full posterior distribution

of chi given the local field d? But if you look at the METI, let me go back, if you look

at the METI likelihood and the prior, the analytical form of the posterior stability

given the local field d will be intractable. So this is the intractable problem. So we

need some approximation inference method, such as Markov-Chamberl-Decalov version inference.

But that traditional approximate method is time-consuming and it requires running on