An Improved Method of Wavelets Basis Image Denoising Using Besov Norm Regularization

This paper proposes art improved image denoising algorithm which bases on wavelets thresholding - and uses the Besov norm regularization. Given a noisy image u
₀
and suppose the target image u belongs to we need to solve the Besov space B
^a

_q
(L
^p
) optimization problem: min ||u||
^q

_B

^a

<sub>q

(L</sub>

^p

<sub>)

+</sub>
lambda/2|| u - u
₀
||
²

_L

²
The existing algorithms used the fixed parameters p, q, a of B
^a

_q
(L
^p
) to determine the threshold of wavelets reconstruction. Since different parts of an image may have different smoothness properties, and wavelet coefficients denote different frequency subbands of an image, the subimages at each wavelets scale level may have distinct smoothness properties. The larger the a is, the smoother the images are in B
^a

_q
(L
^p
). Taking the smoothness index a into account, we try to optimize the alpha
_j
at different wavelet scale j with p,q fixed. Experimental results show that our method achieves better denoising effect with higher PSNR than the alpha fixed method.