Infrared image reconstruction method based on block-sparse compressive sensing and system thereof
The present invention provides an infrared image reconstruction method based on block-sparse compressive sensing. The method includes: a block-sparse representation step: representing consecutive infrared small target image sequences as signals having block-sparse characteristics; a temporal correlation modeling step: modeling a temporal correlation of data between the consecutive infrared small target image sequences under a Bayesian framework; and a signal reconstruction and output step: reconstructing infrared small target images using a sparse learning algorithm and outputting final estimates of the signals. The present invention further provides an infrared image reconstruction system based on block-sparse compressive sensing. According to the technical solution provided in the present invention, in the process of reconstruction by compressive sensing, signals are reconstructed using a correlation of consecutive signals in time, such that the reconstruction precision of a single frame of signal can be improved, and the algorithm running time is significantly reduced.
1. An infrared image reconstruction method based on block-sparse compressive sensing, comprising:
a block-sparse representation step: representing consecutive infrared small target image sequences as signals having block-sparse characteristics;
a temporal correlation modeling step: modeling a temporal correlation of data between the consecutive infrared small target image sequences under a Bayesian framework; and
a signal reconstruction and output step: reconstructing infrared small target images using a sparse learning algorithm and outputting final estimates of the signals.
2. The infrared image reconstruction method based on block-sparse compressive sensing according to claim 1 , wherein the block-sparse representation step specifically comprises:
representing a multiple-measurement vector model Y=ΦX+V using consecutive infrared small target image sequence signals and a block-sparse matrix, where the infrared small target image signals are x,x∈ M×1 , the block-sparse matrix is X={x 1 , x 2 , . . . , x L }, X∈ M×L , Y [y (.1) , . . . , y (.L) ]∈ N×L is an observation matrix, X [x (.1) , . . . , x (.L) ]∈ M×L , Φ∈ N×M is a known dictionary matrix, V is a noise matrix, y (.i) is an i th column of Y, and x (.i) is an i th column of X; and
convert the multiple-measurement vector model into a single-measurement vector model y=Dx+v, where in the multiple-measurement vector model, the block-sparse matrix X is constituted by consecutive frames x i (i=1, 2, . . . , L) having a temporal correlation, x (i.) (i=1, . . . , M) are independent of each other, x (i.) is an i th row of X, let y=vec(Y T )∈ NL×1 , x=vec(X T )∈ ML×1 , where D=Φ⊗I L , I L is an L-dimension unit matrix, and x is a block-sparse signal and may be represented as
x
=
[
x
1
…
x
L
︸
x
T
[
1
]
x
2
…
x
2
L
︸
x
T
[
2
]
…
x
J
-
L
+
1
…
x
J
︸
x
T
[
M
]
]
T
,
where J=M×L.
3. The infrared image reconstruction method based on block-sparse compressive sensing according to claim 2 , wherein the temporal correlation modeling step specifically comprises:
in the multiple-measurement vector model, assuming X i⋅ are independent of each other and comply with a Gaussian distribution: p(X i⋅ ;γ i ,B i )˜N(0,γ i B i ), where a super-parameter γ i controls the sparseness of the vectors X i⋅ , and B i is a positive definite matrix that describes a time correlation structure of X i⋅ and is a parameter to be estimated, assuming a priori of the sparse vector x is p(x;γ i ,B i )˜N(0,Σ 0 ), and modeling a temporal correlation of data between the consecutive infrared small target image sequences under a Bayesian framework, where γ i is a non-negative super-parameter,
Σ
0
=
[
γ
1
B
1
⋱
γ
M
B
M
]
,
and the time structure of the signals is described with a prior density for constructing the matrix B i .
4. The infrared image reconstruction method based on block-sparse compressive sensing according to claim 3 , wherein the signal reconstruction and output step specifically comprises:
under the condition that an observation y is known, obtaining a posterior estimate of the sparse vector x using a Bayesian method: p(x|y;σ 2 ,γ i ,B i )˜N(μ x ,Σ x ), where a Gaussian likelihood function of the observation y is:
p
(
y
|
x
,
σ
2
)
=
(
2
πσ
2
)
-
N
/
2
exp
(
-
1
2
σ
2
y
-
Dx
2
)
,
where
μ
x
=
1
σ
2
Σ
x
D
T
y
where and Σ x =Σ 0 −Σ 0 D T (σ 2 I+DΣ 0 D T ) −1 DΣ 0 ; and
estimating the super-parameter in the above equation through a maximum likelihood method or an expectation maximization method:
γ
i
=
Tr
[
B
-
1
(
Σ
x
i
+
μ
x
i
(
μ
x
i
)
T
)
]
L
,
i
=
1
,
…
,
M
,
B
=
1
M
∑
i
=
1
M
Σ
x
i
+
μ
x
i
(
μ
x
i
)
T
γ
i
,
i
=
1
,
…
,
M
,
σ
2
=
y
-
D
μ
x
2
2
+
σ
′2
[
ML
-
Tr
(
Σ
x
Σ
0
-
1
)
]
NL
,
and outputting final estimates of the signals after the iteration ends.
5. An infrared image reconstruction system based on block-sparse compressive sensing, comprising:
a block-sparse representation module, configured to represent consecutive infrared small target image sequences as signals having block-sparse characteristics;
a temporal correlation modeling module, configured to model a temporal correlation of data between the consecutive infrared small target image sequences under a Bayesian framework; and
a signal reconstruction and output module, configured to reconstruct infrared small target images using a sparse learning algorithm and output final estimates of the signals.
6. The infrared image reconstruction system based on block-sparse compressive sensing according to claim 5 , wherein the block-sparse representation module is specifically configured to:
represent a multiple-measurement vector model Y=ΦX+V using consecutive infrared small target image sequence signals and a block-sparse matrix, where the infrared small target image signals are x,x∈ M×1 , the block-sparse matrix is X={x 1 , x 2 , . . . , x L }, X∈ M×L , Y [y (.1) , . . . , y (.L) ]∈ N×L is an observation matrix, X [x (.1) , . . . , x (.L) ]∈ M×L , Φ∈ N×M is a known dictionary matrix, V is a noise matrix, y (.i) is an i th column of Y, and x (.i) is an i th column of X; and
convert the multiple-measurement vector model into a single-measurement vector model y=Dx+v, where in the multiple-measurement vector model, the block-sparse matrix X is constituted by consecutive frames x i (i=1, 2, . . . , L) having a temporal correlation,) x (i.) (i=1, . . . , M) are independent of each other, x (i.) is an i th row of X, let y=vec(Y T )∈ NL×1 , x=vec(X T )∈ ML×1 , where D=Φ⊗I L , I L is an L-dimension unit matrix, and x is a block-sparse signal and may be represented as
x
=
[
x
1
…
x
L
︸
x
T
[
1
]
x
2
…
x
2
L
︸
x
T
[
2
]
…
x
J
-
L
+
1
…
x
J
︸
x
T
[
M
]
]
T
,
where J=M×L.
7. The infrared image reconstruction method based on block-sparse compressive sensing according to claim 6 , wherein the temporal correlation modeling module is specifically configured to:
in the multiple-measurement vector model, assume X i⋅ are independent of each other and comply with a Gaussian distribution: p(X i⋅ ;γ i ,B i )˜N(0,γ i B i ), where a super-parameter γ i controls the sparseness of the vectors X i⋅ , and B i is a positive definite matrix that describes a time correlation structure of X i⋅ and is a parameter to be estimated, assume a priori of the sparse vector x is p(x;γ i ,B i )˜N(0,Σ 0 ), and model a temporal correlation of data between the consecutive infrared small target image sequences under a Bayesian framework, where γ i is a non-negative super-parameter,
Σ
0
=
[
γ
1
B
1
⋱
γ
M
B
M
]
,
and the time structure of the signals is described with a prior density for constructing the matrix B i .
8. The infrared image reconstruction method based on block-sparse compressive sensing according to claim 7 , wherein the signal reconstruction and output module is specifically configured to:
under the condition that an observation y is known, obtain a posterior estimate of the sparse vector x using a Bayesian method: p(x|y;σ 2 ,γ i ,B i )˜N(μ x ,Σ x ), where a Gaussian likelihood function of the observation y is:
p
(
y
|
x
,
σ
2
)
=
(
2
πσ
2
)
-
N
/
2
exp
(
-
1
2
σ
2
y
-
Dx
2
)
,
where
μ
x
=
1
σ
2
Σ
x
D
T
y
where and Σ x =Σ 0 −Σ 0 D T (σ 2 I+DΣ 0 D T ) −1 DΣ 0 ; and
estimate the super-parameter in the above equation through a maximum likelihood method or an expectation maximization method:
γ
i
=
Tr
[
B
-
1
(
Σ
x
i
+
μ
x
i
(
μ
x
i
)
T
)
]
L
,
i
=
1
,
…
,
M
,
B
=
1
M
∑
i
=
1
M
Σ
x
i
+
μ
x
i
(
μ
x
i
)
T
γ
i
,
i
=
1
,
…
,
M
,
σ
2
=
y
-
D
μ
x
2
2
+
σ
′2
[
ML
-
Tr
(
Σ
x
Σ
0
-
1
)
]
NL
,
and output final estimates of the signals after the iteration ends.