4 Reconstruction of Retinal OCT Images with Sparse Representation
97
patches the positions and values of the nonzero coefficients in
ˆ
α
t
di f,i
T
t1
are different.
Thus, the position information is preserved using T different sequences, while the
value information is stored with other T different sequences, as shown in Fig. 4.16c.
We label the three classes (“Very similar”, “Not very similar”, and “Different”)
of nearby slices as 0, 1, and 2, respectively. These class types are stored in one
sequence. In addition, the means
m
t
i
T
t1
of nearby patches
x
t
i
T
t1
are quantized
and stored into T different sequences. Furthermore, indexes
h
t
i
T
t1
of the selected
sub-dictionaries for nearby patches are stored with another T sequences. Finally, we
apply Huffman coding [59] on the above sequences to create one bit stream. At the
decoding site, given the compressed bit stream, we first extract the mean
m
t
i
T
t1
,
sparse vectors
α
t
i
T
t1
, and indexes
h
t
i
T
t1
of the selected sub-dictionaries for each
set of nearby patches. Then, a set of nearby patches
x
t
i
T
t1
are reconstructed by,
x
t
i D
structural
h
t
i
α
t
i + m
t
i , t 1, . . . , T.
(4.22)
Subsequently, each patch ˆ
x
t s
i (where t s denotes a specific patch) is further enhanced
by weighted averaging of the nearby patches: ˆ
x
t s
i
T
t1
w
t,t s
i ˆ
x
t
i , where w
t,t s
i
[5] is
estimated as:
w
t,t s
i
exp
−
ˆ
x
t
i − ˆ
x
t s
i
2
2
/ h
Norm
.
(4.23)
In (4.13), Norm is defined as
T
t1
exp
−
ˆ
x
t
i − ˆ
x
t s
i
2
2
/ h
and h is a predefined scalar.
Finally, we recover each B-scan by combining its reconstructed patches in a rasterscan order.
4.3.3.3 Experimental Results
To validate the effectiveness of the proposed 3D-ASRC algorithm, we compared
its performance with those of four well-known compression approaches: JPEG
2000, MPEG-4, SPIHT [60], K-SVD [30], and three variants of the proposed algorithm: SRC-Dif, 2D-ASRC, 3D-ASRC-WA. For the SRC-Dif method, we utilize the
“different-patch” based sparse representation and encoding scheme for compression.
For the 2D-ASRC method, we denoted a number of spatial nearby patches within
one slice as the nearby patches. For the 3D-ASRC-WAmethod, we do not use the 3D
weighted averaging technique for the final reconstruction, compared to the 3D-ASRC
method.
In our experiments, we first used volumetric scans of human retinas from 26
different subjects with and without non-neovascular AMD, imaged by an 840-nm
wavelength SDOCT system from Bioptigen, Inc. (Durham, NC, USA) with an axial
97
patches the positions and values of the nonzero coefficients in
ˆ
α
t
di f,i
T
t1
are different.
Thus, the position information is preserved using T different sequences, while the
value information is stored with other T different sequences, as shown in Fig. 4.16c.
We label the three classes (“Very similar”, “Not very similar”, and “Different”)
of nearby slices as 0, 1, and 2, respectively. These class types are stored in one
sequence. In addition, the means
m
t
i
T
t1
of nearby patches
x
t
i
T
t1
are quantized
and stored into T different sequences. Furthermore, indexes
h
t
i
T
t1
of the selected
sub-dictionaries for nearby patches are stored with another T sequences. Finally, we
apply Huffman coding [59] on the above sequences to create one bit stream. At the
decoding site, given the compressed bit stream, we first extract the mean
m
t
i
T
t1
,
sparse vectors
α
t
i
T
t1
, and indexes
h
t
i
T
t1
of the selected sub-dictionaries for each
set of nearby patches. Then, a set of nearby patches
x
t
i
T
t1
are reconstructed by,
x
t
i D
structural
h
t
i
α
t
i + m
t
i , t 1, . . . , T.
(4.22)
Subsequently, each patch ˆ
x
t s
i (where t s denotes a specific patch) is further enhanced
by weighted averaging of the nearby patches: ˆ
x
t s
i
T
t1
w
t,t s
i ˆ
x
t
i , where w
t,t s
i
[5] is
estimated as:
w
t,t s
i
exp
−
ˆ
x
t
i − ˆ
x
t s
i
2
2
/ h
Norm
.
(4.23)
In (4.13), Norm is defined as
T
t1
exp
−
ˆ
x
t
i − ˆ
x
t s
i
2
2
/ h
and h is a predefined scalar.
Finally, we recover each B-scan by combining its reconstructed patches in a rasterscan order.
4.3.3.3 Experimental Results
To validate the effectiveness of the proposed 3D-ASRC algorithm, we compared
its performance with those of four well-known compression approaches: JPEG
2000, MPEG-4, SPIHT [60], K-SVD [30], and three variants of the proposed algorithm: SRC-Dif, 2D-ASRC, 3D-ASRC-WA. For the SRC-Dif method, we utilize the
“different-patch” based sparse representation and encoding scheme for compression.
For the 2D-ASRC method, we denoted a number of spatial nearby patches within
one slice as the nearby patches. For the 3D-ASRC-WAmethod, we do not use the 3D
weighted averaging technique for the final reconstruction, compared to the 3D-ASRC
method.
In our experiments, we first used volumetric scans of human retinas from 26
different subjects with and without non-neovascular AMD, imaged by an 840-nm
wavelength SDOCT system from Bioptigen, Inc. (Durham, NC, USA) with an axial