Due to different reasons, seismic data may have missing traces. Seismic data reconstruction is such a procedure to remove sampling artifacts, and to improve amplitude analysis, which are very important for subsequent processing steps including high-resolution processing, wave-equation migration, multiple suppression, amplitude-versus-offset (AVO) or amplitude-versus-azimuth (AVAZ) analysis, and time-lapse studies Wang et al. (2010); Liu and Sacchi (2004); Zhong et al. (2015); Trad et al. (2002); Naghizadeh and Sacchi (2010); Abma and Kabir (2005). In recent years, due to the development of compressive sensing framework, there are a lot of sparsity-based methods for interpolating irregularly sampled seismic data. However, for regularly missing traces, sparsity-based methods Abma and Kabir (2006); Li et al. (2012); Chen et al. (2014a) can not obtain satisfying results because of the strong aliasing noise in the transform domain. Instead, the prediction-based approaches Naghizadeh and Sacchi (2007); Spitz (1991) are still the best approaches for interpolating regularly missing traces.

In this paper, we propose to use seislet transform to perform a sparsity-based reconstruction, based on the well-established projection onto convex sets (POCS) framework Abma and Kabir (2006). Many numerical studies show that the local slope is the main factor affecting the sparsity and anti-aliasing ability of the seislet transform. Even though with the original aliased data, we can not obtain precise dip estimation, we can use low-pass filtered data (below 15 Hz) to estimate local slope in order to construct the seislet transform of the full-band seismic data and perform thresholding. Synthetic data and field data examples show nearly perfect results using the proposed approach. The traditional prediction based approach and the $F-K$ based POCS approach are both compared with the proposed approach and are demonstrated to be less effective.