Method and a system for compressed ultrafast tomographic imaging
View Patent ↗A method and a system for imaging a transient event, the method comprising passively recording spatiotemporal projections of the transient event in an angular range from −45° to +45°; and processing the recorded spatiotemporal projections by compressed sensing tomographic image reconstruction to recover the transient event. The system comprises an imaging unit and a shearing unit for imaging a dynamic event to different positions, a detector that records data by spatially integrating over each pixel and temporally integrating; and a processing unit that reconstructs the dynamic event from said data by compressed sensing tomographic image reconstruction.
1. A method for compressed ultrafast tomographic imaging of dynamic events, comprising data acquisition and image reconstruction from acquired data; wherein said data acquisition comprises acquiring spatiotemporal projections I(x,y,t) of a dynamic event, temporally shearing the acquired projections and spatiotemporally integrating resulting sheared projections, wherein the dynamic event is directly imaged by a streak camera with shearing velocities v i (i=1, 2, . . . , N) where N is an integer; a 2D readout camera spatially integrates over each pixel and temporally integrates over the exposure time to a snapshot E i , and the spatiotemporal projections of I(x,y,t) are r described in the x-y-t domain as follows:
E=TS I ( x,y,t ),
where E=[E 1 , E 2 , E N ] T and S=[S 1 , S 2 , S N ] T′ , an angle of a i th spatiotemporal projection being
θ
i
=
tan
-
1
(
v
i
❘
"\[LeftBracketingBar]"
v
max
❘
"\[RightBracketingBar]"
)
,
where |v max | is a maximum shearing velocity of the streak camera; and
wherein said image reconstruction comprises building a sparse matrix and recovering the dynamic event by solving an optimization problem defined with an initialization Î 0 =(TS) T E, as follows:
I
^
=
arg
min
I
{
1
2
E
-
TSI
2
2
+
τ
Φ
TV
(
I
)
}
,
where τ is a regularization parameter, and Φ TV (l) is a regularization function of total variation TV; and resulting reconstructed spatiotemporal projections I(x,y,t) of the dynamic event have a sequence depth of N t =rT s , where T s is a sweep time,
r
=
❘
"\[LeftBracketingBar]"
v
max
❘
"\[RightBracketingBar]"
P
c
is an imaging speed, and P c is a pixel size of the readout camera, each frame in the spatiotemporal projections I(x,y,t) having a (x,y) size of N x ≤N b and N y ≤N v −N t +1 pixels N b and N v being horizontal and vertical pixel counts of the readout camera, the reconstruction being done by a processing unit.
2. A method for imaging a transient event, comprising passively recording spatiotemporal projections of the transient event in an angular range from −45° to +45°; and processing the recorded spatiotemporal projections by compressed sensing tomographic image reconstruction to recover the transient event, the method comprising data acquisition and image reconstruction from acquired data; wherein said data acquisition comprises acquiring spatiotemporal projections I(x,y,t) of the transient event, temporally shearing the acquired projections and spatiotemporally integrating resulting sheared projections, wherein the transient event is directly imaged by a streak camera with shearing velocities v i (i=1, 2, N) where N is an integer; a 2D readout camera spatially integrates over each pixel and temporally integrates over the exposure time to a snapshot E i , and the spatiotemporal projections of I(x,y,t) are r described in the x-y-t domain as follows:
E=TS I ( x,y,t ),
where E=[E 1 , E 2 , E N ] T and S=[S 1 , S 2 , S N ] T′ , an angle of a i th spatiotemporal projection being
θ
i
=
tan
-
1
(
v
i
❘
"\[LeftBracketingBar]"
v
max
❘
"\[RightBracketingBar]"
)
,
where |v max | is a maximum shearing velocity of the streak camera; and
wherein said image reconstruction comprises building a sparse matrix and recovering the dynamic event by solving an optimization problem defined with an initialization Î 0 =(TS) T E, as follows:
I
^
=
arg
min
I
{
1
2
E
-
TSI
2
2
+
τ
Φ
TV
(
I
)
}
,
where τ is a regularization parameter, and Φ TV (l) is a regularization function of total variation TV; and resulting reconstructed spatiotemporal projections I(x,y,t) of the dynamic event have a sequence depth of N t =rT s , where T s is a sweep time,
r
=
❘
"\[LeftBracketingBar]"
v
max
❘
"\[RightBracketingBar]"
P
c
is an imaging speed, and P c is a pixel size of the readout camera, each frame in the spatiotemporal projections I(x,y,t) having a (x,y) size of N x ≤N b and N y ≤N v −N t +1 pixels N b and N v being horizontal and vertical pixel counts of the readout camera, the reconstruction being done by a processing unit.
3. The method of claim 2 , comprising using an image-converter streak camera.
4. The method of claim 2 , comprising using a rotating-mirror streak camera.
5. The method of claim 2 , comprising acquiring 2D streak images with different shear velocities; treating the streak images at the different shear velocities as corresponding different angular projections in temporal dimension; and processing the streak images by the compressed sensing tomographic image reconstruction to recover the transient event.
6. The method of claim 2 , comprising temporal shearing and spatiotemporal integration.
7. A system for compressed ultrafast tomographic imaging, comprising an imaging unit, a shearing unit, a detector, and a processing unit; wherein said imaging unit and said shearing unit image a dynamic event to different positions; said detector records data by spatially integrating over each pixel and temporally integrating; and said processing unit reconstruct the dynamic event from said data by compressed sensing tomographic image reconstruction, the system comprising a streak camera imaging the dynamic event by taking N images with shearing velocities v i (i=1, 2, N) where N is an integer; and a 2D readout camera that spatially integrates over each pixel and temporally integrates over the exposure time to a snapshot E i , yielding spatiotemporal projections of I(x,y,t) described in a x-y-t domain as follows:
E=TS I ( x,y,t ),
where E=[E 1 , E 2 , E N ] T and S=[S 1 , S 2 , S N ] T′ , an angle of a i th spatiotemporal projection being
θ
i
=
tan
-
1
(
v
i
❘
"\[LeftBracketingBar]"
v
max
❘
"\[RightBracketingBar]"
)
,
where |v max | is a maximum shearing velocity of the streak camera; wherein said processing image reconstruct the dynamic event by building a sparse matrix and recovering the dynamic event by solving an optimization problem defined with an initialization Î 0 =(TS) T E, as follows:
I
^
=
arg
min
I
{
1
2
E
-
TSI
2
2
+
τ
Φ
TV
(
I
)
}
,
where τ is a regularization parameter, and Φ TV (l) is a regularization function of total variation TV; and resulting reconstructed spatiotemporal projections I(x,y,t) of the dynamic event have a sequence depth of N t =rT s , where T s is a sweep time,
r
=
❘
"\[LeftBracketingBar]"
v
max
❘
"\[RightBracketingBar]"
P
c
is an imaging speed, and P c is a pixel size of the readout camera, each frame in the spatiotemporal projections I(x,y,t) having a (x,y) size of N x ≤N b and N y ≤N v −N t +1 pixels N b and N v being horizontal and vertical pixel counts of the readout camera.
8. The system of claim 7 , wherein said imaging unit and said shearing unit are provided as a streak camera.
9. The system of claim 7 , wherein said imaging unit and said shearing unit are provided as an image-converter streak camera.
10. The system of claim 7 , wherein said imaging unit and said shearing unit are provided as a rotating-mirror streak camera.
11. The system of claim 7 , wherein said shearing unit comprises a galvanometer scanner.
12. The system of claim 7 , wherein said detector is one of: electron-multiplying charge-coupled devices (CCD), complementary metal-oxide-semiconductor (CMOS) cameras, and scientific CMOS cameras.