Instrumentation & Measurement Magazine 24-2 - 50

Fig. 6. An illustration of medical image fusion including two source images and their fusion results obtained by three different methods. (a) The T1-weigted MR
source image. (b) The T2-weigthed MR source image. (c) The fused image of the conventional local and single-component SR-based method [19]. (d) The fused
image of the global SR model, namely, CSR-based method [43]. (e) The fused image of the multi-component CSR (MC-CSR)-based method [46].

in (8) can be solved iteratively over Xc,m and Xt,m by the following two sub-problems:
Sub-problem Xc,m (given the fixed Xt,m):
2

	

Mc
Mc
1
Y   d c ,m  X c ,m  c  X c ,m ,	(9)
1
X c ,m 2

m 1
m 1
2

min

Mt

where Y Y   d t ,m  X t ,m.
m1

Sub-problem Xt,m (given the fixed Xc,m):
2

	

Mt
Mt
1
Y   dt ,m  X t ,m  t  X t ,m ,	(10)
1
X t ,m 2

m 1
m 1
2

min

Mc

where Y Y   d c ,m  X c ,m.
m1

The above two sub-problems both have the same formulation as the CSR model in (6) and thus can be solved by the
related algorithms. In the fusion method presented in [46],
each source image is firstly decomposed using the model in
(8). Then, the obtained sparse coefficient maps of the cartoon
and the texture components from different source images are
fused. Finally, the fused image is reconstructed by the fused
sparse coefficient maps and dictionary filters.
Fig. 6 provides an illustration to show the advantage of
global and multi-component representation in SR-based medical image fusion. The source images to be fused are a pair of
T1-weighted MR image (Fig. 6a) and T2-weighted MR image
(Fig. 6b). Fig. 6c, Fig. 6d and Fig. 6e show their fusion results
obtained by three representative SR-based fusion methods,
which are the conventional local and single-component SRbased method [19], the global SR mode, namely, CSR-based
method [43] and the multi-component CSR (MC-CSR)-based
method [46]. A close-up is given in each image for better observation. It can be seen that the fused image of the conventional
SR-based method suffers from a considerable loss of spatial
details. The CSR-based method alleviates this issue to a significant degree. The MC-CSR-based method further improves the
performance on detail preservation.
50	

Finally, a quantitative comparison on the above three representative SR-based fusion methods is performed. Ten pairs
of multimodality medical images from the Whole Brain Atlas,
a popular database for medical image fusion research created
by Harvard Medical School, is adopted for testing. In [47], Liu
et al. grouped the objective evaluation metrics of image fusion
into four categories: the information theory-based ones, image
feature-based ones, structure similarity (SSIM)-based ones and
human visual system (HVS)-based ones. In this experiment,
one frequently-used metric is selected from each category. The
four metrics adopted are the localized mutual information
(LMI)-based metric QLMI [48], the image gradient-based metric
QG [49], the SSIM-based metric QE [50] and the HVS-based metric QCB [51]. For each metric, a higher score indicates a better
performance. Please refer to [47] for more information about
the objective evaluation of image fusion and [48]-[51] for the
details of these four metrics used. Table 2 lists the quantitative
assessment results, in which the average scores over all the ten
testing samples are reported. We can see that the adoptions of
both global representation and multi-component representation result in obvious increases on all the metrics, indicating
the significance of these improved representations.
In summary, the multi-component and global representations can bring several advantages over the conventional
SR models for image fusion. The separation of different components improves the flexibility in designing effective fusion
strategies. The single-valued property of the CSR model avoids
the accumulating-averaging operation used in the conventional patch-based SR models, leading to better capability in
extracting spatial details from the source images. In addition,
owing to the shift-invariant property, the CSR model has higher
potential for the fusion of mis-registered and noisy regions than

Table 2 - Objective assessment results
of different fusion methods
SR [19]

CSR [43]

MC-CSR [46]

QLMI

0.8413

0.8467

0.8575

QG

0.5616

0.5664

0.6052

QE

0.5690

0.5733

0.6397

QCB

0.6502

0.6662

0.6866

IEEE Instrumentation & Measurement Magazine	

April 2021



Instrumentation & Measurement Magazine 24-2

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