Dictionary learning methods adaptively train their bases from the given data in an iterative manner; hence, they can capture more detailed features and achieve sparser representation than a method that uses a fixed basis. However, there also exists a good chance of erratic noise corrupting the dictionary because of the insufficiency of the L1-norm regularization in distinguishing the signal and erratic noise, causing the inaccuracy of both dictionary learning and its application. A robust dictionary learning method is proposed to reconstruct the missing data even in the presence of strong erratic noise. Specifically, a projected operator, which is constructed with the robust Huber misfit, is used to damp erratic noise to a low-amplitude level. In the dictionary learning step, erratic noise is gradually reduced to an acceptable level with the help of this projected operator, from which the signal prototypes (or atoms) can be safely extracted in each iteration. Then, the learned dictionary is used to iteratively estimate the signal from the noisy and under-sampled data, performing noise attenuation as well as data interpolation at non-recording locations. We test the proposed dictionary learning method using 2D and 3D noisy seismic examples and compare it with other state-of-the-art methods. Numerical results demonstrate its superior effectiveness at recovering missing data and increasing signal-to-noise ratio in the presence of erratic noise.
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