SAOCOM Mission, National Commission of Space Activities (CONAE)
751 P. Colon Ave., C1063ACH Buenos Aires, Argentina
Phone: +54 11 4331-0074 Ext. 439, Fax: +54 11 4331-0074 Ext. 411
Email: [email protected]
Alberto E. Giraldez
Email: [email protected]
In this work, an efficient method for removing speckle (in wavelet domain) of unknown variance from Synthetic Aperture Radar (SAR) images is described. The method is based on the shifting and scaling of the coefficients of the highest wavelet subbands. Specifically, we decompose the speckled SAR image into wavelet subbands, apply shifting and scaling within each high subband, and reconstruct a SAR image from the modified detail coefficients. Despeckling results compare favorably with most methods in use at the moment.
A SAR image is affected by speckle in its acquisition and processing. Image despeckling is used to remove the multiplicative speckle while retaining as much as possible the important signal features. In recent years there has been an important amount of research on wavelet thresholding and threshold selec-tion for SAR despeckling , , because wavelet provides an appropriate basis for separating noisy signal from the image signal. The motivation is that as the wavelet transform is good at energy compaction, the small coefficients are more likely due to noise and large coefficient due to important signal features . These small coefficients can be thresholded without affecting the significant features of the image. Thresholding is a simple non-linear technique, which operates on one wavelet coefficient at a time. In its basic form, each coefficient is thresholded by comparing against threshold, if the coefficient is smaller than threshold, set to zero; otherwise it is kept or modified. Replacing the small noisy coefficients by zero and applying the inverse wavelet transform on the result, we obtain the reconstruction with the essential signal characteristics and with less noise. Since the work of Donoho & Johnstone , there has been much research on finding thresholds, however few are specifically designed for images. Unfortunately, this technique has the following disadvantages:
- it depends on the correct election of the type of thresholding (soft, hard, and semi-soft) or shrinkage, e.g., VisuShrink, SureShrink, OracleShrink, OracleThresh, BayesShrink, Thresholding Neural Network (TNN), etc. -,
- it depends on the correct estimation of the threshold and the distributions of the signal and noise, which are unquestionably the most important design parameters of these techniques,
- the specific distributions of the signal and noise may not be well matched at different scales.
- it does not have a fine adjustment of the threshold after their calculation, and
- it should be applied at each level of decomposition, needing several levels.
Therefore, a new method without these constraints will represent an upgrade.
II. SPECKLE MODEL
Speckle noise in SAR images is usually modelled as a purely multiplicative noise process of the form
Is(r,c) = I(r,c) S(r,c) = I(r,c) [1+ S’(r,c)] = I(r,c) + N(r,c) (1)
The true radiometric values of the image are represented by I, and the values measured by the radar instrument are represented by Is. The speckle noise is represented by S. The parameters r and c means row and column of the respective pixel of the image. If S’(r,c) = S(r,c) – 1 and N(r,c) = I(r,c) S’(r,c), we begin with a multiplicative speckle S and finish with an additive speckle N , which avoid the log-transform, because the mean of log-transformed speckle noise does not equal to zero  and thus requires correction to avoid extra distortion in the restored image. For single-look SAR images, S is Rayleigh distributed (for amplitude images) or negative exponentially distributed (for intensity images) with a mean of 1. For multi-look SAR images with independent looks, S has a gamma distribution with a mean of 1. Further details on this noise model are given in .