Research of Multi-focus Image Fusion Algorithm Based on Sparse Representation and Orthogonal Matching Pursuit - Advances in Image and Graphics Technologies - page 60

winder goes back to the leftmost position and then moves down for one pixel. And so
on, an image of WH × can be divided into ( Wn +−× +− 1) ( Hn 1) image blocks of

.The advantages of using overlapping image blocks are:
1) Images in any size can be divided into blocks without taking boundary treatment
into consideration;
2) It can avoid blocking effects to some extent when taking image reconstruction.
Suppose that there are K image:

nn ×

{}

K

I , and each image is divided into overlapping

i

i1 =

{}

K

image blocks of nn to get P ,in which every column of

P is obtained by

×

i

i1 =

the form of column vector from an image block of nn × . If i I is the image of

{ } { } ( ) ( ) ( )

WH × ,

P is the matrix of

nn ×× +−×+− W n1 H n1 . The m-column

i Xm by sparse
representation based on over-complete dictionary D . If solving the sparse coefficient
of

P

(:, m) of

P can be got its corresponding sparse coefficient

(:, )

{}

K

{}

K

P , we can get K matrixes X .

i i

i1 = i1 =

Coefficients Fusion. Suppose that it exists an image F , with dividing it into blocks to
get P

() F

firstly. And then the sparse coefficient X

() F

can be obtained by sparse

representation. If X

() F

is known, the image F can appear through the inverse

process.
This algorithm uses solved

{}

K

() F F Xm of () (:,

X to get X . The m-column )

i

i1 =

X is replaced by the maximum l norm in the m-column of each matrix in
{}

()

K

X . And the following formulas can be expressed:

( )

i

i1 =

idx = arg max X :, m

i i

1

(4)

()

( ) ( )

F

XmXm :, = :,

idx

() F

The fusion strategy is used to recover per column of X and finally the image

F can be reconstructed by the inverse process.

3

Image Fusion Experiments and Results

3.1 Image Fusion Rules

In the process of the corresponding multi-source image fusion algorithm
implementation, we select four groups of multi-focus test images in this essay, with
two images for each group. For multi-focus images in each group, five classic multi-
source image fusion algorithms (based on FSD Laplacian pyramid transform, Contrast
pyramid transform, DWT with DBSS (2,2) wavelet transform, SIDWT with Haar
translational invariance discrete wavelet transform and spatial frequency fusion
algorithm), sparse representation and orthogonal matching pursuit multi-focus image
fusion algorithm proposed in the paper are applied to do image fusion experiments by
MALAB. To make fused images based on various multi-source fusion algorithms