Adaptive multiple subtraction using a hybrid ℓ2-ℓ1 pattern-learning approach

Abstract

Adaptive multiple subtraction (AMS) is a critical and challenging task for multiple attenuation. Recently, pattern-learning-based AMS approaches, including pattern coding and decoding steps based on the [Formula: see text] norm, have achieved impressive results. However, the traditional pattern-learning approach might hurt the primaries under the minimum energy condition of the [Formula: see text]-norm-based decoding. Thus, we adopt a hybrid [Formula: see text]-[Formula: see text] pattern-learning-based AMS approach, which includes the [Formula: see text]-norm-based multiband coding and the [Formula: see text]-norm-based decoding steps. In the coding stage, the pattern dictionary is obtained by using the [Formula: see text]-norm-based principal component analysis, which has been proven to be an effective feature extraction method. Subsequently, in the decoding stage, the learned patterns from the predicted multiple are used to estimate the multiples in the recorded data, whereas the primaries are treated as additive noise. In general, the primaries are better represented by a Laplacian than by a Gaussian distribution. Consequently, the proposed method uses the [Formula: see text] norm to decode the multiples contained in the recorded data and then uses an alternating split Bregman algorithm to solve the decoding problem. We validate the approach on synthetic and field data sets, and our method yields better results compared with the [Formula: see text]-norm-based matching filter and the traditional pattern-learning approach.