Abstract
With the rapid development of the computer technology，digital image has become one of
the most important media for message exchange.However, in the process of image acquisition
and transmission, because of various reasons, noise interference is inevitable, which could
have massive impact on the subsequent image analysis and the spread of the image
information. So to solve this problem, using image denoising is one of the most foundational
and crucial treatment technology in the field of image processing and computer vision.
As a foundamental mathematical tool the L
0
gradient minimization model has been used
for image smoothing successfully. The most impressive advantage of L
0
gradient
minimization is protecting the salient edges in the image processing. As an improvement of
the total variation (TV) model which employs the L
1
norm of the gradient, the LGM model
performs better when processing images with the feature of piecewise constant. However, just
like the TV model, the LGM model suffers, even more seriously, from the staircase effect and
it fails to well preserve the texture in image.
In recent decades, an image denoising method using the non-parameter data fitting
approach based on the localized least squares has been proposed and has attracts lots of
attention from image processing researchers. The kernel regression(KR) model, the most
representative one, has been proved to present better visual effect and more accurate texture
memory. But this method has the probability of serious flow-like effects and the image edges
often blur because of their excessive smooth boundary.
According to the analysis, the two methods just play complementary roles in the process
of image denoising, so this paper proposes two novel schemes by combining above two
models. The proposed models successfully avoid the disadvantages of both methods.
First, this paper introduces an new effective fidelity term (KR) into the LGM model(L
0
gradient minimization-kernel regression , LGM-KR). It is demonstrated that the proposed
method presents the promising ability to remove the noise by numbers of experiments,
meanwhile, the edges and texture information is well preserved.
Second, we extend the LGM-KR model by replacing L
0
gradient minimization by L
0
two-order partial derivative minimization, and the extended model is used for image
denoising combined with KR model. As a result, this scheme has more predominant
performance due to the high-order feature.
Key words：image denoising, L
0
gradient minimization, kernel regression, L
0
two-order
partial derivative minimization
