Denoising one-dimensional signals with curvelets and contourlets

Fast Fourier Transforms (FFTs) and Discrete Wavelet Transformations (DWTs) have been routinely used as methods of denoising signals. DWT limitations include the inability to detect contours, curves and directional information of multi-dimensional signals. In the past decade, two new approaches have surfaced: curvelets, developed by Candès; and contourlets, developed by Do et al. The typical applications of contourlets and curvelets include two-dimensional image data denoising. We explore the use of curvelets and contourlets to the one-dimensional (1D) denoising problem. Working with seismic data, we introduce various types of data noise and the wavelet, curvelet, and contourlet transforms are applied to each signal. We tested multiple decomposition levels and different thresholding values. The benchmark for determining the effectiveness of each transform is the peak signal-to-noise ratio (PSNR) between the original signal and the denoised signal. The proposed denoising methods demonstrate contourlets and curvelets as a viable alternative to the DWT and FFT during signal processing. The initial results indicate that the contourlet and curvelet methods yield a higher PSNR and lower error than the DWT and FFT for 1D data.