A method of combining coherence-constrained sparse coding and dictionary learning for denoising

Abstract

We have addressed the seismic data denoising problem, in which the noise is random and has an unknown spatiotemporally varying variance. In seismic data processing, random noise is often attenuated using transform-based methods. The success of these methods in denoising depends on the ability of the transform to efficiently describe the signal features in the data. Fixed transforms (e.g., wavelets, curvelets) do not adapt to the data and might fail to efficiently describe complex morphologies in the seismic data. Alternatively, dictionary learning methods adapt to the local morphology of the data and provide state-of-the-art denoising results. However, conventional denoising by dictionary learning requires a priori information on the noise variance, and it encounters difficulties when applied for denoising seismic data in which the noise variance is varying in space or time. We have developed a coherence-constrained dictionary learning (CDL) method for denoising that does not require any a priori information related to the signal or noise. To denoise a given window of a seismic section using CDL, overlapping small 2D patches are extracted and a dictionary of patch-sized signals is trained to learn the elementary features embedded in the seismic signal. For each patch, using the learned dictionary, a sparse optimization problem is solved, and a sparse approximation of the patch is computed to attenuate the random noise. Unlike conventional dictionary learning, the sparsity of the approximation is constrained based on coherence such that it does not need a priori noise variance or signal sparsity information and is still optimal to filter out Gaussian random noise. The denoising performance of the CDL method is validated using synthetic and field data examples, and it is compared with the K-SVD and FX-Decon denoising. We found that CDL gives better denoising results than K-SVD and FX-Decon for removing noise when the variance varies in space or time.

3-D Seismic Noise Attenuation via Tensor Sparse Coding With Spatially Adaptive Coherence Constraint

“…In the process of seismic data acquisition, the ideal tensor is observed in the presence of random noise [28], thus the mathematical model is given by…”

“…To overcome the above difficulty, the threshold of sparsity needs to be independent of the noise variance [45]. For the consideration of satisfying this condition, [28] exploited the coherence threshold of residual R with respect to the dictionary D. Extending this to the tensor version, we propose the TSC-SAC model to solve these two problems, constraining the sparsity by tensor spatially adaptive coherence.…”

“…However, the fixed basis is determined in advance, which can lead to an unsuitable adjustment to the varying strength of seismic noise. The SC-based method encodes several basic elements as linear combinations in the dictionary domain, controlling the sparsity with a set threshold value to attenuate the seismic noise, including the K-singular value decomposition (K-SVD) [24], the datadriven tight frame (DDTF) [25], the double-sparsity dictionary learning [26], the multichannel singular spectrum analysis (MSSA) [27], and the coherence-constrained sparse coding [28]. Nevertheless, the mentioned method has difficulty in eliminating spatio-temporal noise virtually, due to the deficiency of spatial information in seismic data.…”

A Patch Based Denoising Method Using Deep Convolutional Neural Network for Seismic Image

“…have been designed for seismic random noise reduction to meet the demands of the development in seismic exploration, such as wavelet transform-based denoising methods [1], [2], time-frequency peak filters [3]- [5], sparse representation [6], PDE-based diffusion filters [7], [8]. Although these denoising methods highly improve the quality of seismic images, the denoising performances still need to be improved under the condition of low SNR and spatiotemporally variant seismic random noise.…”

Coherent noise suppression by learning and analyzing the morphology of the data

“…For more efficient training, DDTF, sparse K-SVD, and SuKro learn structured dictionaries: In DDTF, the dictionary is constrained to be a tight frame; in sparse K-SVD, the atoms are constructed as sparse linear combinations of predefined basis functions; and in SuKro, the learned dictionary is a sum of the Kronecker products of smaller dictionaries. The DL methods have proven to perform well for denoising seismic data (Beckouche and Ma, 2014;Liang et al, 2014;Yu et al, 2015Yu et al, , 2016Zhu et al, 2015;Turquais et al, 2017). Another data-driven method, the Cadzow filtering method (Trickett, 2002(Trickett, , 2008, also called singular spectrum analysis (SSA) (Sacchi, 2009;Chen and Sacchi, 2015), uses rank reduction for denoising.…”