Entropy field decomposition for image analysis
A system and method for analysis of complex spatio-temporal data utilize complimentary general approaches to data analysis: information field theory (IFT), which reformulates Bayesian theory in terms of field theory in order to incorporate the important and often overlooked conditions that ensure continuity of underlying parameter spaces that are to be estimated from discrete data, and entropy spectrum pathways (ESP), which uses the principle of maximum entropy to incorporate prior information on the structure of the underlying space in order to estimate measures of connectivity.
1. A method for analysis of complex spatio-temporal data, the method comprising, in a computer processor:
receiving image data from an image detector, wherein the image data comprises points within a lattice;
ranking a plurality of optimal paths within the lattice according to path entropy, wherein the rankings are arranged in a coupling matrix;
using eigenvalues and eigenvectors from the coupling matrix to construct an information Hamiltonian;
determining mode amplitudes corresponding to spatially and temporally interacting modes of the information Hamiltonian; and
generating an output comprising a display of the mode amplitudes.
2. The method of claim 1 , wherein the information Hamiltonian is of the form
H
(
d
,
a
k
)
=
-
j
k
†
a
k
+
1
2
a
k
†
Λ
a
k
+
∑
n
=
1
∞
1
n
!
∑
k
1
K
…
∑
k
n
K
Λ
~
k
1
…
k
n
(
n
)
a
k
1
…
a
k
n
,
where matrix Λ is the diagonal matrix Diag{λ 1 , . . . , λ K } composed of eigenvalues of a noise corrected coupling matrix, a k is an amplitude of the kth mode, and j k is the amplitude of the kth mode in the expansion of the source j.
3. The method of claim 2 , wherein the mode amplitudes are determined according to the relationship
Λ
a
k
=
(
j
k
-
∑
n
=
1
∞
1
n
!
∑
k
1
K
…
∑
k
n
K
Λ
~
kk
1
…
k
n
(
n
+
1
)
a
k
1
…
a
k
n
)
.
4. The method of claim 1 , wherein the image detector comprises a magnetic resonance imaging system and the complex spatio-temporal data comprises functional magnetic resonance image (FMRI) data, and wherein the mode amplitudes correspond to functional tractography and functional eigentracts.
5. The method of claim 1 , wherein the image detector comprises a Doppler radar system and the complex spatio-temporal data comprises Doppler radar data, and wherein the mode amplitudes correspond to tilt, stretch and vorticity.
6. A method for analysis of complex multivariate spatio-temporal data, comprising:
receiving in a computer processor image data from an image detector, wherein the image data comprises a plurality of voxels; and
causing the computer processor to perform the steps of:
ranking pathways between voxels according to path entropy and generating a coupling matrix therefrom;
determining eigenvalues and eigenvectors for the coupling matrix;
constructing an information Hamiltonian using eigenvalues and eigenvectors;
determining mode amplitudes corresponding to spatially and temporally interacting modes of the information Hamiltonian; and
generating an output comprising a display of the mode amplitudes.
7. The method of claim 6 , wherein the information Hamiltonian is of the form
H
(
d
,
a
k
)
=
-
j
k
†
a
k
+
1
2
a
k
†
Λ
a
k
+
∑
n
=
1
∞
1
n
!
∑
k
1
K
…
∑
k
n
K
Λ
~
k
1
…
k
n
(
n
)
a
k
1
…
a
k
n
,
where matrix Λ is the diagonal matrix Diag{λ 1 , . . . , λ K } composed of eigenvalues of a noise corrected coupling matrix, a k is an amplitude of the kth mode, and j k is the amplitude of the kth mode in the expansion of the source j.
8. The method of claim 6 , wherein the mode amplitudes are determined according to the relationship
Λ
a
k
=
(
j
k
-
∑
n
=
1
∞
1
n
!
∑
k
1
K
…
∑
k
n
K
Λ
~
kk
1
…
k
n
(
n
+
1
)
a
k
1
…
a
k
n
)
.
9. The method of claim 6 , wherein the image detector comprises a magnetic resonance imaging system and the complex spatio-temporal data comprises functional magnetic resonance image (FMRI) data, and wherein the mode amplitudes correspond to functional tractography and functional eigentracts.
10. The method of claim 6 , wherein the image detector comprises a Doppler radar system and the complex spatio-temporal data comprises Doppler radar data, and wherein the mode amplitudes correspond to tilt, stretch and vorticity.