Inverse halftoning techniques are known to introduce visible distortions (typically, blurring or noise) into the reconstructed image. To reduce the severity of these distortions, we propose a novel training approach for inverse halftoning algorithms. The proposed technique uses a coupled dictionary (CD) to match distorted and original images via a sparse representation. This technique enforces similarities of sparse representations between distorted and non-distorted images. Results show that the proposed technique can improve the performance of different inverse halftone approaches. Images reconstructed with the proposed approach have a higher quality, showing less blur, noise, and chromatic aberrations.