 This
image is a denoising experiment using the curvelet
transform. The original image is a synthetic noise-free
seismogram simulated from a one-dimensional velocity model,
courtesy of Felix Herrmann and Eric Verschuur.
|
|
 |
 |
 |
 |
|
(1)
|
(2)
|
(3)
|
(4)
|
Image (1) is a zoom-in. In real life, however, seismic
data is corrupted by noise. In
Image (2), we simulate degradation
by adding gaussian white noise with standard deviation equal
to one tenth of the total intensity, PSNR = 20.0 dB. Image
(3) is the result of standard translation-invariant wavelet
thresholding (see WaveLab), PSNR = 30.8 dB. Image
(4) is the result of curvelet thresholding, PSNR = 37.6
dB. |
|
The lesson of this experiment is that curvelets are an
adequate tool to represent bandlimited wavefronts
in an efficient manner, such as those present in reflection
seismology data.
For reference, the
transform used to generate these images is the FDCT via
wrapping, complex-valued and with curvelets at the finest
scale. The CurveLab toolbox contains, among others, an
'enhanced denoise' demo which tests the same thresholding
algorithm on another image.
|
|
