COSMIC:
Compressed Sensing
for Magnetic Resonance
Imaging & Cosmology
Philippe Ciuciu (I2BM) & Jean-Luc Starck (IRFU)
October 19th, 2016
UNIRS | 03-02-2016
| PAGE 1
MRI CONTEXT IN COSMIC
RADIO-INTERFEROMETRY CONTEXT IN COSMIC
COMMONALITIES BETWEEN MRI & RADIOINTERFEROMETRY
• Data sampling in the 2D/3D Fourier domain:
k-space
MR Image
Linear
Reconstruction
Acquisition
IFFT
7Tesla MRI Scanner
@NeuroSpin
Spatial frequencies
COMMONALITIES BETWEEN MRI & RADIOINTERFEROMETRY
• Sampling in the 2D Fourier domain:
COMMON ISSUE: NEED FOR SPARSE SAMPLING
• High resolution imaging requires collecting too much data
• Temporally-resolved hyperspectral imaging necessary to recover
fast transient sources
A common need for Compressed Sensing
Data is sparse, compressible, redundant…
Sense the compressed information directly!
Donoho, Tao,
Romberg, Candes
COSMIC: SCIENTIFIC OBJECTIVES
 Magnetic Resonance Imaging
Compressed Sensing (CS-MRI)
Fourier space
MR Image
Nonlinear
Data
Image
reconstruction
7Tesla (NeuroSpin) acquisition
7T MRI scanner@NeuroSpin
Random undersampling
Sparsity in wavelet basis
Fourier space
Galaxy image (Cygnus A)
 Radio-interferometry
m s
250
225
45 00
200
acquisition
175
30
150
m s
125
44 00
100
Image
reconstruction
75
30s
m
50
25
s
+ 40° 43 00
33s
30s
27s
RA (J2000)
19h 59m24s
0
Jy/beam
Dec (J2000)
Data
Nonlinear
s
COSMIC: MAJOR STAKES FOR CEA & DRF
• MRI (11.7 Tesla magnet at NeuroSpin, ISEULT project)
 60 millions of investment for the strongest machine worldwide
 Optimal exploitation based on CS: imaging better and faster
 Disruptive technology transferable to industry (Siemens, GE …)
 Partnerships with Europe (Germany) and US (CMRR)
• Radio-interferometry (Squared Kilometer Array telescope)
 Positioning on the biggest array telescope worldwide
 Big data analysis (Data deluge: SKA will acquire 9 Tb/s,
more than Google !!! and 1PB per day in the archive)
COSMIC: ISSUES & LOCKS UP (1/4)
• MRI: Optimize image representation & increase sparsity
Redundant transforms
𝜱 induces sparser
decompositions 𝜶
Curvelets
Starlets, shearlets
CosmoStat
NeuroSpin
COSMIC: ISSUES & LOCKS UP (2/4)
• MRI: Optimize image reconstruction
• Synthesis formulation (eg, FISTA):
• Analysis formulation (eg, ADMM):
Observation model:
• Equivalence between synthesis & analysis formulations for wavelet bases
• Faster algorithms for the analysis formulation with redundant transforms
• Extensions to 3D imaging & multi-channel data
CosmoStat
NeuroSpin
COSMIC: ISSUES & LOCKS UP (3/4)
• Radio-interferometry: Optimize measurement matrix
NeuroSpin
CosmoStat
COSMIC: ISSUES & LOCKS UP (4/4)
• Computational aspects:
 Scalability of 2D reconstruction algorithms to 3D imaging
 Addressing the case of non-Cartesian Fourier data
 Parallel programming on multi-CPU and GPU architectures
using the most convenient languages (Python, Julia) on
top of C/C++ libraries
NeuroSpin
CosmoStat
COSMIC: AGENDA & DELIVERABLES
Hiring master trainees:
- Sylvain Lannuzel (ECP+M2R)
- …
CosmoStat
NeuroSpin
D1:Improved 2D reconstruction
09/2016
D3: In-vivo Human
D4: (2D+t) & 3D imaging
acquisitions
12/2016
04/2017
09/2017
10/2016
M1: Kick-off
Meeting
M2: Advances on
MRI reconstruction
…
…
…
…
M3: Gain in performance
& scalability
D5: Gadgetron
demonstrator
New PhD student:
Loubna El Gueddari
NeuroSpin
M4: Wrap-up
CosmoStat
D2: Parallel programming (code analysis, acceleration)
COSMIC CONSORTIUM: NEUROSPIN TEAM
NeuroSpin (UNATI-UNIRS)
Ph. Ciuciu (leader) A. Vignaud
Expertise in:
- MR Physics & signal processing
- Design of CS schemes
- Non-Cartesian reconstruction
- Parallelization of algorithms (GPU)
C. Lerman
CS in MRI
Neuroimaging scientist
MR Physicists
C. Lazarus
A. Coste
PhD Student
PhD Student
CS-MRI
CS-MRI
A. Grigis
Engineer
COSMIC CONSORTIUM: COSMOSTAT TEAM
Expertise in:
- Astronomy and Signal processing
- 2D/3D sparse decompositions
- Modeling of prior informations
- Inverse problem solving
Astrophysics Division (CosmoStat)
J.-L. Starck (leader) J. Bobin
F. Sureau
CS in Astronomy
Research Director
S. Pires
Sparse image analysis
M. Jiang
J. Girard
PhD Student
Euclid scientist
CS in Astronomy
Radio-astronomer
COSMIC CONSORTIUM: JOINING OUR EFFORTS
Nurtering interactions
in Compressed
Sensing
NeuroSpin (UNATI-UNIRS)
Ph. Ciuciu (leader) A. Vignaud
Neuroimaging scientist
C. Lerman
MR Physicists
C. Lazarus
A. Coste
PhD Student
PhD Student
CS-MRI
CS-MRI
A. Grigis
Astrophysics Division (CosmoStat)
J.-L. Starck (leader) J. Bobin
Research Director
S. Pires
F. Sureau
Sparse image analysis
M. Jiang
J. Girard
PhD Student
Engineer
Euclid scientist
CS in Astronomy
Radio-astronomer
CONCLUSION