Improving Mutual Coherence with Non-Uniform Discretization of Orthogonal Function for
188
Image Denoising Application
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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
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100
150
200
250
300
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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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