Research of Multi-focus Image Fusion Algorithm Based on Sparse Representation and Orthogonal Matching Pursuit - Advances in Image and Graphics Technologies - page 58

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all focus objects are clear from those K images. If  represents the fusion

operator, the multi-focus image fusion can be described by the following formula:
(

⇅

)

 (1)
As to the multi-focus image, the classic multi-source image fusion algorithms
(based on FSD pyramid image fusion algorithm[2-4], DWT image fusion
algorithm[5], the contrast pyramid image fusion algorithm, SIDWT image fusion
algorithm[6-7] and the spatial frequency fusion algorithm[8-11]) are still adopted to
deal with the corresponding image fusion which can be evaluated subjectively and
objectively. Five common objective evaluation indicators include mutual
information(MI), average gradient(AG), correlation coefficient(CC), distorted
degree(DD) and Q ab/f . The experimental results suggest that the effects of those
common multi-source focus image fusion algorithms are not ideal, this is why, in this
essay, we propose a multi-focus image fusion algorithm based on sparse
representation and orthogonal matching pursuit.

F = I

1 ,, , k

I … I

2 Multi-focus Image Fusion Algorithm Based on Sparse

Representation

2.1 Image Sparse Representation and Orthogonal Matching Pursuit

Algorithm

The core of sparse representation is that signals can be approximated by the linear
combination of a small number of columns in the over-complete dictionary D (each
column in D is also called an atom). But how to obtain the coefficient of the linear
combination becomes the main problem of sparse representation, and the following
formula can be described:

2

min x , subject to y − Dx ≤  (2)

0 2

In formula 2, x represents l to calculate numbers of non-zero components in

0

vector x , and is allowable approximation error.

However, solving formula 2 to make x satisfy Φ

∈

is a NP-hard problem
without being solved accurately in computer time. But thanks to the efforts of
scientists, the above problem resolution has been transformed from the unsolvable l
minimization to a minimizing model of solving l by some convex optimization
algorithms, such as interior point method[12], gradient projection method[13-14],
greedy algorithm[15-16], iterative threshold method[17-18] and Bregman iteration
based on Bregman distance[19]. Recently, the iterative greedy algorithm has attracted
much attention by its low complexity and simple geometric explanation, aiming to
obtain reconstruction by the support of iteration to calculate x . It mainly includes
matching pursuit: MP [20], orthogonal matching pursuit: OMP[21], stagewise
orthogonal matching pursuit: StOMP[22], regularized orthogonal matching pursuit:
ROMP[23], compressive sampling matching pursuit: CoSaMP[24], subspace pursuit:
SP[25] and improved backward optimized OMP: IBOOMP [26], etc.

y = x