Motion compensated reconstruction

Transcription

1 Motion compensated reconstruction Educational course: Image acquisition and Reconstruction 25th Annual meeting of the ISMRM, Honolulu, 2017 Sajan Goud Lingala Siemens Healthineers, Princeton, USA

2 Declaration of Financial Interests or Relationships Speaker Name: Sajan Goud Lingala I have the following financial interest or relationship to disclose with regard to the subject matter of this presentation: Company Name: Siemens Healthineers Type of Relationship: Employee

3 Outline Introduction Explicit motion constrained recovery schemes Generalized reconstruction of inverted coupled systems (GRICS) Motion compensated Compressed Sensing -- Sparsity, low rank based Applications Challenges Heuristic based implicit motion constrained recovery schemes Data sorting XD GRASP Next talk: Manifold approaches

4 Outline Introduction Explicit motion constrained recovery schemes Generalized reconstruction of inverted coupled systems (GRICS) Motion compensated Compressed Sensing -- Sparsity, low rank based Applications Challenges Heuristic based implicit motion constrained recovery schemes Data sorting XD GRASP Manifold based implicit methods: next talk

5 Introduction Occurrence of motion is common in several MRI exams Head motion J. Pipe et al, 99

6 Introduction Occurrence of motion is common in several MRI exams Head motion Cardiac arrhythmias J. Pipe et al, 99 Courtesy: Andrew Yoon, USC

7 Introduction Occurrence of motion is common in several MRI exams Head motion Cardiac arrhythmias Breathing motion J. Pipe et al, 99 Courtesy: Andrew Yoon, USC Courtesy: Li Feng, NYU

8 Motion and k-space k-space acquired in time Image Fourier Transform s x = X k S k e ikx D. Atkinson, ISMRM 2010

9 Motion and k-space k-space acquired in time Image Fourier Transform s x = X k S k e ikx The sum in the Fourier Transform implies that motion at any time can affect every pixel D. Atkinson, ISMRM 2010

10 k-space corrections for affine motion Image motion k-space effect Translation (rigid shift) Rotation Expansion General affine Phase ramp Rotation (same angle) Contraction Affine transform A(x) = A x+t A V!V 0 k 0 = A T k F(k) = ei2 (k0 t) det(a) F 0 (k 0 ) D. Atkinson, ISMRM 2010

11 k-space corrections for affine motion Image motion k-space effect Translation (rigid shift) Rotation Expansion General affine Phase ramp Rotation (same angle) Contraction Affine transform A(x) = A x+t A V!V 0 k 0 = A T k F(k) = ei2 (k0 t) det(a) F 0 (k 0 ) D. Atkinson, ISMRM 2010

12 k-space corrections for affine motion Image motion k-space effect Translation (rigid shift) Rotation Expansion General affine Phase ramp Rotation (same angle) Contraction Affine transform A(x) = A x+t A V!V 0 k 0 = A T k F(k) = ei2 (k0 t) det(a) F 0 (k 0 ) D. Atkinson, ISMRM 2010

13 k-space corrections for affine motion Image motion k-space effect Translation (rigid shift) Rotation Expansion General affine Phase ramp Rotation (same angle) Contraction Affine transform A(x) = A x+t A V!V 0 k 0 = A T k F(k) = ei2 (k0 t) det(a) F 0 (k 0 ) D. Atkinson, ISMRM 2010

14 Non-rigid motion Most physiological motion is non-rigid Not straightforward to directly correct in the k-space Royuela et al., MRM 2015

15 Motion corrected reconstruction: early approaches Problem of combining k-space shots that are at different motion states Artifact free image Measured data Shot 1 (t1) Shot 2 (t2) Shot 3 (t3) k-space min ke( ) bk 2 2 Forward model: Motion, Coil sensitivities, etc. Motion profile Motion state 1 Motion state 2 Motion state 3 PG. Batchelor et al., MRM 2005; F. Odille et al., MRM 2008

16 Motion corrected reconstruction: early approaches Knowledge of forward model }E - Forward model Artifact free image PG. Batchelor et al., MRM 2005; F. Odille et al., MRM 2008

17 Motion corrected reconstruction: early approaches Knowledge of forward model }E - Forward model Artifact free image Measured data min ke( ) bk 2 2 Forward model: Motion, Coil sensitivities, etc. Artifact free image Least squares problem PG. Batchelor et al., MRM 2005; F. Odille et al., MRM 2008

18 Motion corrected reconstruction: early approaches Knowledge of forward model E - Forward model } Artifact free image Measured data min ke( ) bk 2 2 Forward model: Motion, Coil sensitivities, etc. Artifact free image Least squares problem Solved by Conjugate Gradients PG. Batchelor et al., MRM 2005; F. Odille et al., MRM 2008

19 Motion estimation External measures respiratory bellows, optical tracking, etc. Explicit Navigator based measures pencil beam navigator, FID navigators, central k-space lines, etc. Self-navigated approaches PROPELLER, radial, spiral trajectories, etc. Motion models Joint estimation of motion and reconstruction parameters D. Atkinson, ISMRM 2010

20 Motion estimation External measures respiratory bellows, optical tracking, etc. Explicit Navigator based measures pencil beam navigator, FID navigators, central k-space lines, etc. Self-navigated approaches PROPELLER, radial, spiral trajectories, etc. Motion models Joint estimation of motion and reconstruction parameters D. Atkinson, ISMRM 2010

21 Motion estimation External measures respiratory bellows, optical tracking, etc. Explicit Navigator based measures pencil beam navigator, FID navigators, central k-space lines, etc. Self-navigated approaches PROPELLER, radial, spiral trajectories, etc. Motion models Joint estimation of motion and reconstruction parameters D. Atkinson, ISMRM 2010

22 Motion estimation External measures respiratory bellows, optical tracking, etc. Explicit Navigator based measures pencil beam navigator, FID navigators, central k-space lines, etc. Self-navigated approaches PROPELLER, radial, spiral trajectories, etc. Motion models Joint estimation of motion and reconstruction parameters D. Atkinson, ISMRM 2010

23 Retrospective reconstruction of cine images using iterative motion correction M. Hansen et al., MRM 2011

24 Retrospective reconstruction of cine images using iterative motion correction Deformation due to respiration estimated from low temporal resolution data M. Hansen et al., MRM 2011

25 Retrospective reconstruction of cine images using iterative motion correction Deformation due to respiration estimated from low temporal resolution data M. Hansen et al., MRM 2011

26 Retrospective reconstruction of cine images using iterative motion correction } M. Hansen et al., MRM 2011 Free breathing

27 Joint estimation of motion and reconstruction Parameterizing motion based on motion sensor signals (eg. bellows) MX u(r,t) {z } = m (r) {z } S m (t) {z } displacement fields i=1 motion parameters motion sensors Optimization: min, ke( ) sk µ 1 R( )+µ 2 R( ) } } } data consistency regularization on motion parameters regularization on image F. Odille et al., MRM 2008

28 Joint estimation of motion and reconstruction Parameterizing motion based on motion sensor signals (eg. bellows) MX u(r,t) {z } = m (r) {z } S m (t) {z } displacement fields i=1 motion parameters motion sensors Generalized reconstruction of inversion coupled systems (GRICS): min, ke( ) bk µ 1 R( )+µ 2 R( ) } } } data consistency regularization on motion parameters regularization on image F. Odille et al., MRM 2008

29 Joint estimation of motion and reconstruction min, ke( ) bk 2 + µ 2 1 R( )+µ 2 R( ) {z } C(, ) Motion estimation Reconstruction min C(, n ) min C( n, ) F. Odille et al., MRM 2008

30 Joint estimation of motion and reconstruction min, ke( ) bk 2 + µ 2 1 R( )+µ 2 R( ) {z } C(, ) Motion estimation Reconstruction min C(, n ) min C( n, ) Coarse to fine resolution strategies are commonly used to avoid local minima Convergence: only empirical F. Odille et al., MRM 2008

31 Improving constrained reconstruction with motion correction

32 Improving constrained reconstruction with motion correction Example of myocardial perfusion data with motion Original Deformation corrected S.G.Lingala, IEEE-TMI, 2015 *Data acquired in accordance with IRB approval, University of Utah

33 Improving constrained reconstruction with motion correction Example of myocardial perfusion data with motion Original Deformation corrected S.G.Lingala, IEEE-TMI, 2015 *Data acquired in accordance with IRB approval, University of Utah

34 Improving constrained reconstruction with motion correction Deformation corrected data is more sparse/compact in transform domains Temporal FFT Smoother temporal gradients With motion With motion Motion compensated Motion compensated Fewer significant singular values Fewer nonzero coeffs.

35 Formulation - Low rank S.G.Lingala, IEEE-TMI, 2015

36 Variable splitting and continuation strategies Original problem {f, } =min f, ka(f) bk2 2 + k (T f)k`1; (1) { data consistency { temporal regularization Splitting allows to decouple deformation estimation from reconstruction min f,,g ka(f) bk2 2 + k (g)k`1; s.t., T f = g;

37 Variable splitting and continuation strategies Modified cost function min f,,g ka(f) bk2 2 + k (g)k`1; s.t., T f = g; Penalize the quadratic violation by introducing a parameter apple min ka(f) bk2 + 2 f,,g k (g)k`1 + 2 kt f gk 2 2 Is equivalent to the original cost when tends to 1

38 Variable splitting and continuation strategies Modified cost function min f,,g ka(f) bk2 2 + k (g)k`1; s.t., T f = g; Penalize the quadratic violation by introducing a parameter apple min ka(f) bk2 + 2 f,,g k (g)k`1 + 2 kt f gk 2 2 Is equivalent to the original cost when tends to 1

39 Alternate between well defined subproblems Continuation: Iterate while gradually increasing min g D min f D min g k (g)k`1 + 2 kt f {z } ˆf gk 2 2 min f ka(f) bk kt f gk 2 2 Denoising/dealiasing step Reconstruction update min D minkt f gk 2 2 Image registration

40 Demonstration of robustness to initialization with continuation strategies S.G.Lingala, IEEE-TMI, 2015 *Data acquired in accordance with IRB approval, University of Utah

41 Fully sampled R=3.75 R=4.5 R=5.6 R=7.5 Deformation corrected temporal finite difference Temporal Finite Difference S.G.Lingala, IEEE-TMI, 2015 *Data acquired in accordance with IRB approval, University of Utah

42 Methods: Motion-compensated Regional Sparsity Block low rank sparsity with motion guidance (BLOSM) ANTS non-rigid registration Coarse to fine resolution correction Block low rank constraint t y x SVD 2E+04 1E+04 8E+03 4E+03 threshold xy 0E Singular values X Chen et al. MRM 2014;72(4): Chen X. et al. MRM 2014;72(4): t

43 Results: Prospective Rate-4 Acceleration Block low rank sparsity with motion guidance (BLOSM) BLOSM Moderate respiratory motion BLOSM Severe respiratory motion Free breathing myocardial perfusion MRI X Chen et al. MRM 2014;72(4): Chen X. et al. SCMR/EuroCMR Joint Scientific Session 2015 Oral *IRB approved study at University of Virginia

44 Motion corrected CS: free breathing cardiac cine Free breathing No Motion Correction Motion Corrected Sparse SENSE (MC-SS) Free breathing Breath-hold (BH) End-diastolic volume (ml) Proposed Method Reference Proposed vs. reference End-systolic volume (ml) Proposed vs. reference BH MC BH MC BH MC BH MC (BH + MC)/2 Stroke Volume (ml) Proposed vs. reference (BH + MC)/2 Ejection fraction (%) Proposed vs. reference 2 min acquisition 2 min acquisition 10 min acq. (including BHs recovery) (BH + MC)/2 (BH + MC)/2 M.Usman et.al, MRM 2011

45 1.6 year female (beta thalassemia with iron overload) CS Conventional CS & PI waf Soft-gated CS & PI w/ autofocusing RT Prospective respiratory trig/gated Resolution: 0.9x1.3x1.6 mm 3 Contrast: Gadavist Scan times: CS,SG,wAF: 29.6 sec RT: sec JY Cheng et al, Young Investigator Award, ISMRM

46 Challenges: Explicit motion estimation and corrected reconstruction Involves non-convex optimization No convergence guarantees Continuation strategies are crucial to monitor convergence Coarse to fine, variable splitting, etc. Increased computation times due to additional motion estimation step Prior guess of motion estimates, coarse-fine correction, GPUs, parallel computing, etc. Interpolation errors while correcting for large deformation errors Modified Jacobian weighting in regularization (Royuela, 2016) Royuela et al., MRM 2015 Royuela et al., MRM 2016

47 Challenges: Explicit motion estimation and corrected reconstruction Involves non-convex optimization No convergence guarantees Continuation strategies are crucial to monitor convergence Coarse to fine, variable splitting, etc. Increased computation times due to additional motion estimation step Prior guess of motion estimates, coarse-fine correction, GPUs, parallel computing, etc. Interpolation errors while correcting for large deformation errors Modified Jacobian weighting in regularization (Royuela, 2016) Royuela et al., MRM 2015 Royuela et al., MRM 2016

48 Challenges: Explicit motion estimation and corrected reconstruction Involves non-convex optimization No convergence guarantees Continuation strategies are crucial to monitor convergence Coarse to fine, variable splitting, etc. Increased computation times due to additional motion estimation step Prior guess of motion estimates, coarse-fine correction, GPUs, parallel computing, etc. Interpolation errors while correcting for large deformation errors

49 Challenges: Explicit motion estimation and corrected reconstruction Involves non-convex optimization No convergence guarantees Continuation strategies are crucial to monitor convergence Coarse to fine, variable splitting, etc. Increased computation times due to additional motion estimation step Prior guess of motion estimates, coarse-fine correction, GPUs, parallel computing, etc. Interpolation errors while correcting for large deformation errors Modified Jacobian weighting in regularization (Royuela, 2016)

50 Implicit motion corrected reconstruction: Reordering prior based Reorder intensities of signal estimate based on prior reconstruction (eg. CS based) Sparsity/Low rank constraint applied on the reordered data set Reordering prior (known) min f ka(f) bk k (R f)k 1 ; G.Adluru et al., Int Journal Biomedical Imaging, 2008 G.Adluru et al., Med Physics 2016 Sparsifying operator Temporal Fourier Transform Temporal finite difference Spectral operators for PCA

51 Implicit motion corrected reconstruction: Reordering prior based Reorder intensities of signal estimate based on prior reconstruction (eg. CS based) Sparsity/Low rank constraint applied on the reordered data set Reordering prior (known) min f ka(f) bk k (R f)k 1 ; G.Adluru et al., Int Journal Biomedical Imaging, 2008 G.Adluru et al., Med Physics 2016 Sparsifying operator Temporal Fourier Transform Temporal finite difference Spectral operators for PCA

52 Reordering based prior: 1D example A rapidly varying fully sampled signal and its sorted version Reconstruction without reordering (R=2) Reconstruction with reordering (R=2) G.Adluru et al., Int Journal Biomedical Imaging, 2008 G.Adluru et al., Med Physics 2016

53 Sparsity based re-ordering prior Example of myocardial perfusion MRI Fully sampled Without reordering R=2.5 With reordering R=2.5 G.Adluru et al., Int Journal Biomedical Imaging, 2008 G.Adluru et al., Med Physics 2016 *IRB approved study at University of Utah

54 XD-GRASP: A Simple Example Motion averaging Motion state 1 Motion state 2 Motion state n Motion State 1 Motion State 2 Motion State n Feng L et al. ISMRM 2015 p568 Courtesy: Li Feng, NYU School of Medicine

55 XD-GRASP: A Simple Example Motion averaging Motion state 1 Motion state 2 Motion state n z An extra respiratory dimension x t Temporal sparsity y Feng L et al. ISMRM 2015 p568 Courtesy: Li Feng, NYU School of Medicine

56 XD-GRASP Reconstruction 2 x = arg min E x y + λ S x + λ S x x x S 1 S 2 : Multidimensional images to be reconstructed : Sparsifying transform along the 1 st temporal dimension : Sparsifying transform along the 2 nd temporal dimension z y: Sorted k-space E : Encoding function (multicoil) λ: Regularization parameters x y t Res Contrast enhancement t Cardiac motion Multiple echoes Flow encoding Courtesy: Li Feng, NYU School of Medicine

57 XD-GRASP for DCE-MRI of the Liver Z projection Liu J et al. MRM (5): Spinc le P et al (6): Pang J et al. MRM (5):

58 Respiratory Motion-Resolved DCE-MRI XD-GRASP GRASP Motion State 1 Motion State 2 Motion State 3 Motion State 4

59 Conclusions Explicit Motion estimation and compensation methods can address the motion sensitivity of current sparsity/low rank based models Continuation strategies are used for well behaved convergence Increased computation times and nontrivial interpolation artifacts remain a challenge Implicit motion constrained recovery methods show promise to address the challenges with explicit methods

60 Acknowledgements Slides from Li Feng, NYU School of Medicine Xiao Chen, Siemens Healthineers Muhammad Usman, Kings College London Javier Royuela del Val, University of Valladolid Ganesh Adluru, University of Utah Joseph Cheng, Stanford University Andrew Yoon, University of Southern California