Instrumentation & Measurement Magazine 24-2 - 46

Literature
Review

Fig. 2. The typical schematic diagram of medical image fusion methods.

strategy that can be further divided into several steps including activity level measurement, fusion rule and consistency
verification [13]. Finally, the fused image is reconstructed
by performing the corresponding inverse transform on the
merged coefficients. The multi-scale decomposition (MSD)based fusion methods have been a mainstream in this field
since their appearance in 1980s-90s. A variety of MSD approaches including image pyramids, wavelets, curvelets,
coutourlets and shearlets have been widely applied to design
medical image fusion methods [14]. During the last decade,
sparse representation (SR)-based methods have emerged as
an influential branch in image fusion [15], demonstrating
promising potential to obtain better fusion results than conventional MSD-based methods. Therefore, this paper mainly
focuses on providing an overview of the recent advances on
SR-based medical image fusion methods. The articles participated in this overview are collected from the Web of Science
Core Collection Database during the last ten years, since the
first work [16] in this field was proposed in 2010. The keywords used for initial searching mainly include " medical
image fusion, " " image fusion, " " sparse representation, " etc.
The obtained candidates are then screened by studying their
specific contents.

According to the characteristics of adopted SR
models, we can classify the
existing SR-based medical
image fusion methods into
four major categories: local and single-component SR-based
ones, multi-component SR-based ones, global SR-based ones,
and simultaneous global and multi-component SR-based
ones. Table 1 lists a summary of SR-based medical image fusion methods and the literature review of each category is
provided below.

Conventional Local and Single-component
SR-based Methods
The SR theory is believed to be consistent with the physiological characteristics of the human visual system via addressing
the natural sparsity of signals [17]. The basic assumption of
SR is that a signal can be approximately expressed as a linear
combination of a " few " atoms from an over-complete dictionary. Mathematically, given a signal y ∈ n and a dictionary D ∈
n×m
(n < m), the goal of SR is to obtain a sparse vector x ∈ m with
only a few nonzero entries such that y ≈ Dx, which can be formulated as an optimization problem [18]:
	

min x
x

0

s.t. y  Dx

2

  ,	(1)

where  0 denotes the L0-norm that counts the number of
non-zero entries and ε is the error tolerance. A commonly used

Table 1 - A summary of SR-based medical image fusion methods
Category

Model

Features

Local and single-component
SR-based

Orthogonal matching pursuit (OMP) [16],
Simultaneous OMP (SOMP) [19], group
sparse representation (GSR) [21], subdictionary based adaptive SR [22], [23],
[25], [26], combined with other transforms
[27]-[29]

Conventional models: simple and easy to
solve;
Single-component: limited flexibility in
designing fusion strategy;
Multi-valued: limited capability in detail
preservation;
Shift-variant: low robustness to misregistration and noise

Multi-component SR-based

Joint sparse representation (JSR) [34]-[36],
morphological component analysis
(MCA) [37]

Multi-component: higher flexibility in
designing fusion strategy

Global SR-based

Convolutional sparse representation (CSR)
[43], [45]

Single-valued: better capability in detail
preservation;
Shift-invariant: more robust to misregistration and noise

MCA-extended version of CSR [46]

Multi-component: higher flexibility in
designing fusion strategy;
Single-valued: better capability in detail
preservation;
Shift-invariant: more robust to misregistration and noise

Simultaneous multicomponent and global
SR-based

46	

IEEE Instrumentation & Measurement Magazine	

April 2021



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