Dictionary learning based on dip patch selection training for random noise attenuation

In recent years, sparse representation is seeing increasing application to fundamental signal and image-processing tasks. In sparse representation, a signal can be expressed as a linear combination of a dictionary (atom signals) and sparse coefficients. Dictionary learning has a critical role in obtaining a state-of-the-art sparse representation. A good dictionary should capture the representative features of the data. The whole signal can be used as training patches to learn a dictionary. However, this approach suffers from high computational costs, especially for a 3D cube. A common method is to randomly select some patches from given data as training patches to accelerate the learning process. However, the random selection method without any prior information will damage the signal if the selected patches for training are inappropriately chosen from a simple structure (e.g., training patches are chosen from a simple structure to recover the complex structure). We have developed a dip-oriented dictionary learning method, which incorporates an estimation of the dip field into the selection procedure of training patches. In the proposed approach, patches with a large dip value are selected for the training. However, it is not easy to estimate an accurate dip field from the noisy data directly. Hence, we first apply a curvelet-transform noise reduction method to remove some fine-scale components that presumably contain mostly random noise, and we then calculate a more reliable dip field from the preprocessed data to guide the patch selection. Numerical tests on synthetic shot records and field seismic image examples demonstrate that the proposed method can obtain a similar result compared with the method trained on the entire data set and obtain a better denoised result compared with the random selection method. We also compare the performance using of the proposed method and those methods based on curvelet thresholding and rank reduction on a synthetic shot record.