In seismic data processing, denoising and reconstruction are the two steps for identification of resources in the earth subsurface layers. The seismic data quality is affected by random noise and interference during acquisition. Further, the noisy data may be incomplete with missing traces. In this work, we propose a method for incomplete seismic data denoising and reconstruction based on double sparsity dictionary learning (DSDL) with structure oriented filtering (SOF). The main function of the DSDL step is denoising and SOF is used for residual noise attenuation and filling the missing data points. The proposed method is tested on 2-D synthetic and field datasets. The test results show that the DSDL-SOF method has better noise attenuation and reconstruction in terms of signal-to-noise ratio and mean squared error as compared to existing methods.