Application of total-variation-based curvelet shrinkage for three-dimensional seismic data denoising

Transform-based denoising methods are popularly used in image and signal processing, including seismic data processing. However, they often suffer from unwanted artifacts, e.g., nonsmooth edges and pesudo-Gibbs phenomena. A total variation (TV) minimization technique has the ability to suppress these artifacts, particularly in the vicinity of discontinuities. In this letter, we employ the almost optimal sparse transform for seismic data, i.e., curvelet transform, to represent and denoise seismic cubes, combining a projected TV technique as a postprocessing method, in order to reduce unwanted nonsmooth artifacts caused by the curvelet transform. We shrink seismic noise via retaining the significant curvelet coefficients, but for the small ones under a given threshold, we modify them by searching for the minimization of their TV values, instead of setting them to zeros, i.e., TV-combined curvelets with adjustment of small curvelet coefficients by TV minimization. We prove its validity in seismic denoising by comparing with existing methods, including curvelets, TV denoising, and TV-combined curvelets with adjustment of large curvelet coefficients by TV minimization. Numerical experiments show that seismic noise is effectively suppressed by the present technique and that nonsmooth artifacts caused by the curvelet transform are also reduced significantly.