Instrumentation & Measurement Magazine 24-2 - 47

algorithm to solve this problem is the orthogonal matching
pursuit (OMP) [18], which iteratively updates the sparse vector by selecting the atom most relevant to the given signal.
Another popular approach to solve the SR model is relaxing it
to an unconstrained convex form as:
	

min
x

2
1
y  Dx   x ,	(2)
2
1
2

where λ is the regularization parameter.
Owing to the powerful signal representation ability, SR
has achieved great success in various image processing and
computer vision problems. In 2010, Yang and Li first introduced SR into the field of multi-source image fusion [16]. In
their method, the sliding window technique is applied to divide each source image into a large number of overlapping
patches, and sparse decomposition is performed on each patch
independently with the orthogonal matching pursuit (OMP)
algorithm. Then, The L1-norm of the sparse coefficient vector is calculated as the activity measure and the maximum
selection fusion rule is adopted to obtain the fused sparse coefficient vector. Finally, the fused patch is reconstructed by the
fused sparse vector and the dictionary. To construct the entire
fused image, all the fused patches are pasted in their corresponding positions and the intensity value of an overlapped
pixel is averaged by its accumulative times. Fig. 3 shows the
schematic diagram of the above fusion method, which quickly
became a widely used framework in the subsequent studies on
SR-based image fusion.
Since then, a variety of improved SR-based image fusion
methods have been proposed in the literature. In [19], to ensure that image patches from different source images at the
same position are represented by the same subset of dictionary
atoms, the simultaneous OMP (SOMP) algorithm is employed
for sparse decomposition of source images. Instead of constructing a dictionary via analytical models (e.g., DCT bases)
in [16], the K-SVD algorithm [20] is adopted to learn a dictionary from a large number of natural image patches in [19]. Li
et al. proposed a medical image fusion method by introducing a group sparse representation (GSR) model [21], which
can force the non-zero elements to occur in clusters by incorporating the group sparsity constraint into the SR model.

Fig. 3. A widely used schematic diagram for SR-based image fusion.
April 2021	

Liu et al. introduced an adaptive sparse representation (ASR)
model for image fusion [22]. Instead of learning a highly redundant dictionary for sparse decomposition, the ASR model
learn a set of more compact sub-dictionaries in different gradient directions, aiming to alleviate the difficulty in fusing
images corrupted by noises. During the fusion process, one
sub-dictionary is adaptively selected based on the gradient information of input image patches. A similar work that adopts
adaptive sparse domain selection based on image gradient
was proposed by Zong and Qiu in [23]. Unlike the above methods that apply an offline dictionary learning manner, they
employed the online dictionary learning (ODL) algorithm
[24] to learn a set of sub-dictionaries directly from the source
images. Besides supervised classification of image patches,
unsupervised patch clustering based sub-dictionary learning
approaches were also proposed for SR-based image fusion [25,
26]. In these methods, image patches are firstly clustered and
each cluster is then used to train a sub-dictionary. Finally, all
the learned sub-dictionaries are combined to construct a single
dictionary for sparse decomposition.
In addition to the original spatial domain of source images,
SR-based fusion approach has also been applied to merge the
coefficients obtained by some other image transforms. These
fusion methods are known as hybrid transform based methods
[13], as they are based on the combination of different transforms. The main motivation of these methods is to combine
the advantages of different transforms. In [27], Liu et al. introduced the SR-based fusion approach for the low-frequency
components of a multi-scale transform such as Laplacian
pyramid (LP), discrete wavelet transform (DWT) and nonsubsampled contourlet transform (NSCT), which can preserve
image energy more effectively than traditional pixel-wise averaging fusion rule. Zhu et al. proposed a multimodality image
fusion method based on cartoon-texture decomposition and
sparse representation [28], in which the SR-based fusion approach is applied to merge the texture components of source
images. Singh and Anand proposed a hybrid transform based
medical image fusion method [29], in which the SR-based fusion approach is applied to fuse the low-frequency coefficients
obtained by nonsubsampled shearlet transform (NSST).
Another direction in the study of SR-based image fusion
is integrating other image
processing tasks such as
denoising, super-resolution and enhancement into
the fusion framework. Yin
et al. proposed a simultaneous image fusion and
super-resolution framework based on sparse
representation [30]. The
fused sparse coefficients of
low-resolution source images are used to reconstruct
a high-resolution fused
image via a set of learned

IEEE Instrumentation & Measurement Magazine	47



Instrumentation & Measurement Magazine 24-2

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