Blended or simultaneous source shooting is becoming more widely used in seismic exploration and monitoring, which can provide significant uplift in terms of acquisition quality and economic efficiency. Effective deblending techniques are essential to make use of existing processing and imaging methodologies. When dealing with coarse and/or irregularly sampled blended data, the aliasing noise of incomplete data will affect the deblending process and the crosstalk in the blended data will also have a negative influence on the process of data reconstruction. Thus, we have developed a joint deblending and data-reconstruction method using the double-focal transformation to eliminate blending noise and aliasing noise in the coarse, blended data. Numerically blended synthetic and field-data examples demonstrate the validity of its application for deblending and data reconstruction. We also investigate the effect of random noise on the recovery process, and it shows that the algorithm would obtain optimum results after applying a denoising process before deblending and data reconstruction.