## Program of the month: sfthreshold

November 12, 2014 Programs No comments

sfthreshold filters the input by soft thresholding (shrinkage).

Soft thresholding is a point-by-point operation, which can be described mathematically as
$T_{\mu}[u] = \left\{\begin{array}{rcl} u – \mu\,\mbox{sign}(u) & \quad & \mbox{if}\,|u| > \mu \\ 0 & \quad & \mbox{if}\,|u| \le \mu\end{array}\right.$

Soft thresholding was analyzed by Donoho (1995) and became particularly popular thanks to the iterative shrinkage-thresholding algorithm by Daubechies et al. (2004).

Donoho, D. L. (1995). De-noising by soft-thresholding. Information Theory, IEEE Transactions on, 41(3), 613-627.

Daubechies, I., Defrise, M., & De Mol, C. (2004). An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on pure and applied mathematics, 57(11), 1413-1457.

The following example from tccs/seislet/lena shows an image (Seismic Lena) and its reconstruction after soft thresholding in the seislet domain using 5% thresholding (pclip=5).

sfthreshold uses percentage parameter pclip= to set thresholding at the corresponding quantile of the data values. To do soft or hard thresholding with a fixed threshold, use sfthr.

An alternative thresholding-like operation is provided by sfsharpen.

## Seismic data analysis using SSWT

November 12, 2014 Uncategorized No comments

Time-frequency (TF) decomposition is used for characterizing the non-stationary relation between time and instantaneous frequency, which is very important in the processing and interpretation of seismic data. The conventional time-frequency analysis approaches suffer from the contradiction between time resolution and frequency resolution. A new time-frequency analysis approach is proposed based on the synchrosqueezing wavelet transform (SSWT). The SSWT is an empirical-mode-decomposition-like tool but uses a different approach in constructing the components. With the help of the synchrosqueezing techniques, the SSWT can obtain obvious higher time and frequency resolution. Synthetic examples show that the SSWT based TF analysis can exactly capture the variable frequency components. Field data tests show the potential of the proposed approach in detecting anomalies of high-frequency attenuation and detecting the deep-layer weak signal.