Section: New Results

SAR image denoising using an irregularity-preserved denoising technique based on the global Höllder exponent

Participants : Jacques Lévy-Vehel, Yue Huang

This work addresses the speckle noise reduction for SAR images by using the irregularity-preserved denoising technique proposed in [34]. This irregularity preserving denoising scheme in [34] may be summarized as a three-step process in the following:

1. Apply a Discrete Wavelet Transform (DWT) on the noisy signal and represent the resulting coefficients distribution over scales. Estimate the cut-off scale and the global Hölder exponent ${\alpha }_f$ using linear regression of ${max}_k({log}_2|〈f,{\psi }_{j,k}〉\left|\right)$ at larger scales.

2. Extrapolate the larger scale regression line to smaller scales and limit coefficient at smaller scales ($j\ge j_{\text{cut-off}}$) to the boundary value obtained from the linear regression

3. Reconstruct the filtered signal from the set of modified coefficients

where $f$ is the signal under analysis, ${\psi }_{j,k}$ is the wavelet basis, and $〈f,{\psi }_{j,k}〉$ is the wavelet coefficient of $f$ at scale $j$ and location $k$. As it has been shown by simulations in [34], to retrieve irregular signals affected by additive noise, this technique outperforms conventional denoising techniques that apply hard or soft thresholding to the wavelet coefficients.

Considering a speckle-affected SAR image, a complex SAR signal may be represented by:

where $l$ represents one of $L$ realizations, and the noise term $u\left(l\right)$ follows a complex circular centered Gaussian white distribution with unit variance, i.e. $u\sim {𝒩}_C(0,1)$, $E\left(u\left(i\right)u^{*}\left(j\right)\right)={\delta }_{(i-j)}$. The texture of SAR image significantly depends on the backscattering power $\sigma \left(l\right)={\left|y\left(l\right)\right|}^2$.

We aim to use the irregularity-preserved denoising technique to denoise SAR image and enhance its texture. We tested firstly on the simulated signals affected by multiplicative noise and then on real SAR images. This denoising scheme showed potential to reduce the speckle noise, preserve the irregularity of image texture and enhance target signature.

Although the results have been compared with other SAR speckle filtering techniques, we still need more efforts for validation. As long as the results are validated, the work will be written in a paper.