In this paper, we propose to use seislet domain percentile thresholding to iteratively reconstruct the regularly missing seismic traces based on the well-established POCS framework. Numerical tests show that the local slope is the main factor affecting the sparsity and anti-aliasing ability of seislet transform. We update the local slope every several iterations and use low-frequency constrained data to prepare the local slope. We use both synthetic and field data examples to show nearly perfect reconstruction results using the proposed approach for reconstructing regularly missing traces. However, the $F-K$ based POCS approach cannot interpolate the irregularly missing traces because of the strong aliasing noise in the $F-K$ domain. The performance of the proposed approach is better than the commonly used $F-X$ prediction based interpolation approach.