Introduction to Medical Imaging Week 7: Deconvolution and Introduction to Medical Imaging Week 7: Deconvolution and Motion Correction Guy Gilboa Course

Topics Deconvolution and Correcting of motion artifacts in MRI and CT Classical global deblurring Smart acquisition – MRI, CT Rigid and non-rigid motion correction

Convolution Many physical phenomena can be modeled as a convolution with a blur kernel.

Deconvoltion We would like to invert the blur and to recover the underlying data. Deconvolved PET scan Cell Microscopy

1D Deconvolution used in CT and MRI Perfusion CT Perfusion of a person with a stroke

Fourier filtering A classical solution is to use inverse filtering in the Fourier domain ◦ Not a stable solution ◦ Very sensitive to noise Wiener filter – takes into account the noise and signal power-spectrum. ◦ Not very good for images with respect to edge preservation. ◦ Result can oscillate (unphysical data).

Richardson-Lucy Deconvolution A simple and straightforward iterative way for deconvolution. A maximum-likelihood approach which is targeted for Poisson noise. Works quite well for high-SNR scenarios. If the input data is non-negative, none of the further estimates will be negative. Not regularized – tends to converge to somewhat noisy solutions (before convergence sometimes results are better).

Richardson-Lucy Application Simulated Multiple Star Note – super-resolved result and identification of a 4th component Super-resolution means recovery of spatial frequency information beyond the cut-off frequency of the measurement system. measurement PSF reconstruction Taken from slides by Julian C. Christou, Center for Adaptive Optics

Richardson-Lucy Application Simulated Galaxy Truth Diffraction limited SNR = 2500SNR = 250SNR = iterations200 iterations26 iterations All images on a logarithmic scale PSF R-L works best for high SNR

Classical TV deblurring Global known blurring kernel h, the solution u is the minimizer of: ◦ Reminder Blind deconvolution, the solution pair (u,h) is the minimizer of ◦ Initial guess of K (example a delta function). Iterate until convergence: ◦ Fix h, minimize u. ◦ Fix u, minimize h. A non-convex problem → a local minimum is found.

How does a global motion kernel looks like? Standard motion blur Taken from “Deblur using two-phase kernel estimation for robust motion deblurring”, Xu, Jia, ECCV 2010.

More complex motion pattern (and more extreme blur)

The Motion Correction Problem Reconstruct an image with moving organs acquired within a time range, as if it was acquired at a single time- point, without motion artifacts.

Common cases of motion Rigid ◦ Translation, rotation. ◦ Motion of head, arms, legs.. Non-rigid ◦ More complex body motions, different in each region. ◦ Cardiac-motion, respirations.

Common approaches in MRI Prospective Motion Correction: ◦ e.g. PROMO, real-time gradient adjustment, gating, triggering. Retrospective Motion Correction: ◦ mathematical approaches focusing on data consistency. Data Acquisition Strategies: ◦ e.g. PROPELLER sequence, radial/spiral sampling, fast-imaging techniques.

PROPELLER ( PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) Main idea: ◦ Oversampling of the k-space center. ◦ Obtaining multiple fast low-frequency samples of the object. ◦ The samples can then be aligned and corrected in k-space to reduce global motion artifacts (caused by rotation, translation). Pipe, James G. "Motion correction with PROPELLER MRI: application to head motion and free-breathing cardiac imaging." Magnetic Resonance in Medicine42.5 (1999):

PROPELLER k-space

PROPELLER-3 Without correction k-space after correction corrected image

PROMO - PROMO - real-time PROspective MOtion correction in MRI using image-based tracking (2010) Real-time gradient adjustment. Based on a fast acquired low-resolution White, Nathan, et al. "PROMO: Real ‐ time prospective motion correction in MRI using image ‐ based tracking." Magnetic Resonance in Medicine 63.1 (2010): Low resolution “spiral-navigator” measurements used to track the head

PROMO principles Keep the measurement coordinate system fixed with respect to the patient throughout the entire scan process. Image-based approach for prospective motion correction, which utilizes three orthogonal two-dimensional acquisitions, along with a flexible image-based tracking method. Tracking is based on the extended Kalman filter algorithm for online motion measurement.

PROMO - example

PROMO - k-space view

MRI Siemens Syngo BLADE motion correction (PROPELLER technique)

BLADE examples (2006)

Cardiac CT – nonrigid motion Fast gantry rotation 180 degree acquisition Many slices, large coverage (8cm up to even 16cm). Expensive CT ScannerGantry rotation [s] Slices (row-detectors) Coverage [cm] Cardiac Standard~

Cardiac and respiratory gating Periodic motion ECG gating ◦ Prospective – live, less radiation. ◦ Retrospective – easier but with more radiation dose. ◦ ed.virginia.edu/courses/rad/cardiacmr/Techniq ues/Gating.html ed.virginia.edu/courses/rad/cardiacmr/Techniq ues/Gating.html

ECG gating Model shows retrospective ECG gating versus prospective ECG gating. With retrospective gating, the intensity-modulated x-ray beam is on for the entirety of the R-R intervals during imaging. With prospective gating, the x-ray beam is on for about 26% of every other R-R interval. [Shuman WP et al. (2008) Prospective versus retrospective ECG gating for 64-detector.. Radiology Aug;248(2):431-7]

ECG Gating CT result

GE Snapshot Freeze - Cardiac CT (2014) T#tabs/tabED43906F2F A048F3CD9 GE brochure: “While gantry speed alone cannot completely freeze coronary motion, especially at high heart rates, SnapShot Freeze is designed to deliver: 6X improvement in motion artifacts Equivalent Gantry Rotation of 0.058sec Effective Temporal Resolution of 29msec”

SnapShot Freeze concepts Raw cardiac CT data is processed off-line. Cardiac multiphase reconstruction is performed. Automated coronary vessel tracking. The algorithm uses information from adjacent cardiac phases within a single cardiac cycle to characterize vessel motion (both path and velocity) to determine the actual vessel position at the prescribed target phase and adaptively compensate for any residual motion at that phase, effectively compressing the reconstruction temporal window. This approach works on per-vessel and per-segment bases to correct for differing degrees of motion for each voxel of the coronary vessel.

GE “SnapShot Freeze”, intelligent coronary motion correction