Improving Mutual Coherence with Non-Uniform Discretization of Orthogonal Function for

188

Image Denoising Application

0 2 4 6810 12 1416

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cardinality of the Solution

Pr o b ab ility of Success

N ormal Distribut ion Dictionary

Uniform Distribution Dictionary

Cardinality of the Solution

Probability of the Soccess

Figure 2. Comparison of two type dictionary design in exact

sparse recovery.

10 15 202530 35 40 45 50

0

50

100

150

200

250

300

350

Nois e Level

Required Tim e F or Denoising (sec ond)

Normal Distribution

Uniform Di stribution

Normal Distribution

Uniform Distri bution

Figure 3. Time required for denoising process for two type

dictionary design.

The uniform DST dic tionary

The non-uniform DS T dic tionary

(a) (b)

Figure 4. (a) uniform DST dictionary, (b) non-uniform

(normal) DST dictionary.

compared to the uniform one. Normal distribution is used

for sampling and its parameters (mean and standard de-

viation) are optimized through some optimization proce-

sses. Proposed method design has some advantage in

sparse coding and we show this result with plotted the

probability of success in exact sparse recovery. In this

framework we showed that this type of dictionary design

has better performance than uniform sample dictionary

design in image denoising application with improving the

PSNR of result image and decrease the required time for

image denoising. As mention in paper, we can apply this

type redundant dictionary design on any orthogonal set

and also we can use other distribution for sampling the

interval of function definition.

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