The Application of Wavelet-Based Contourlet Transform on Compressed Sensing - Multimedia and Signal Processing - page 572

Fig. 1. schematic plots of contourlet transform and WBCTaa schematic plot of the con-
tourlet transform using 3 LP levels and 4-3-3directional levels.bA schematic plot of the
WBCT using 3 dyadic wavelet levels and 4-3-3directional levels.

3 The Reconstruction Method of Block Compressed Sensing

Using WBCT

As applied to 2D images, CS faces two main difficulties: one is enormous computa-
tion encountered in reconstruction procedure; the other is huge storage requirement in
order to store the random sampling operator. In this paper, we adopt the framework
of block compressed sensing(BCS)[11]. In this framework, the original image is
divided into a certain number of blocks depending on rows and columns of the image
and each block is sampled independently using the same measurement operator
matching the size of the blocks. This method provides comparable performances
compared to existing CS strategies with much lower implementation cost and makes
the real time image processing possible.
In BCS scheme first an image with N = I × I

pixels is divided into blocks of size
B×B each. We can assign B to 16 or 32. Suppose that x i is a vector representing
block i. Sample x i with the same measurement operator

r c

Φ

. Then the corres-

B

y = Φ x

Φ M × B

2

ponding y i is where is an orthonormal measurement

i B i

B B

M

2

B

M = ⌊

⌋ . Here M is the times of CS measurement and the size matrix with

N

of M should meet the principle of Restricted Isometry Property[1,2]. We get M CS
values after BCS operation.