Footprint removal from seismic data with residual dictionary learning

Abstract

<jats:p> Dictionary learning (DL) is a machine learning technique that can be used to find a sparse representation of a given data set by means of a relatively small set of atoms, which are learned from the input data. DL allows for the removal of random noise from seismic data very effectively. However, when seismic data are contaminated with footprint noise, the atoms of the learned dictionary are often a mixture of data and coherent noise patterns. In this scenario, DL requires carrying out a morphological attribute classification of the atoms to separate the noisy atoms from the dictionary. Instead, we have developed a novel DL strategy for the removal of footprint patterns in 3D seismic data that is based on an augmented dictionary built upon appropriately filtering the learned atoms. The resulting augmented dictionary, which contains the filtered atoms and their residuals, has a high discriminative power in separating signal and footprint atoms, thus precluding the use of any statistical classification strategy to segregate the atoms of the learned dictionary. We filter the atoms using a domain transform filtering approach, a very efficient edge-preserving smoothing algorithm. As in the so-called coherence-constrained DL method, the proposed DL strategy does not require the user to know or adjust the noise level or the sparsity of the solution for each data set. Furthermore, it only requires one pass of DL and is shown to produce successful transfer learning. This increases the speed of the denoising processing because the augmented dictionary does not need to be calculated for each time slice of the input data volume. Results on synthetic and 3D public-domain poststack field data demonstrate effective footprint removal with accurate edge preservation. </jats:p>

Improved Low-Rank Tensor Approximation for Seismic Random Plus Footprint Noise Suppression

“…Therefore, as depicted in Fig. 1(a), the noisy data Y are treated as a mixture of the ground-truth image X, footprint noise F, and random noise N. Furthermore, given that acquired footprint noise and random noise are additive [26], the deterioration process caused by footprints and random noise can be stated as follows.…”

“…where P (X) and P (F) denote the priors concerning the clear seismic image and footprint components, respectively, and both τ and λ denote regularization parameters. To date, the two most typically used techniques, explicit filtering [1], [9]- [17] and SR [18]- [26], have been advanced for footprint suppression. From these methods, it can be seen that the key to footprint noise reduction is to build an appropriate model for clean images and footprints, which significantly facilitates the separation of the two components.…”

“…Great efforts have been made by the geophysics community to boost the development of footprint noise removal approaches in recent decades [1], [9]- [26]. Notably, a surplus of vital approaches has been advanced in the seismic literature, and they are roughly grouped into two categories: filtering [1], [9]- [17] and sparse representation (SR) methods [18]- [26]. Filtering methods are the most extensively used techniques and can be divided into two classes: wavenumber/frequency-domain and time-domain filtering.…”

“…Compared to the wavenumber/frequency-domain approaches, SR has been suggested to achieve more compact representations of both clear seismic images and footprints, which allows them to be better separated in the sparsifying domain [18]- [26]. Depending on how correctly the utilized dictionaries are formed, SR methods can be divided into analytical sparsifying transforms and data-driven sparse coding (SC) approaches.…”

“…Entirely unlike analytical sparsifying transforms, considering that the atoms of the learned dictionary are found to represent clear images and footprint patterns [23], [24], SC-based denoising methods naturally deal with these learned atoms and ignore the role of sparse coefficients. In particular, SC methods consider a footprint suppression problem as a binary pattern classification [23]- [25] or filtering task [26] for all learned atoms, which enables the separation of footprints and clear images at the atom level. However, although the existing methods have achieved great progress in footprint removal, their performance relies on handcrafted priors and may be degraded if the input seismic image has unexpected properties beyond the model assumptions.…”