Image Recovery from Incomplete Walsh Measurements Based on Orthogonal Matching Pursuit

Orthogonal matching pursuit (OMP) is a common reconstruction technique for sparse signal, which greedily calculates an estimated value for the original signal. Although OMP is fast and suitable for large sized applications, it requires a large number of measurements and suffers from low reconstruction accuracy. Many research suggested improving its reconstruction quality by transforming the image to the sparse domain; however this method increases the computational complexity especially at the encoding side. In this research, the Walsh measurement matrix is suggested to be applied directly on the image without any transformation to enhance the performance of the OMP technique. The use of the Walsh matrix reduces the computational complexity by getting rid of a transformation step at the encoder, and improves the OMP reconstruction accuracy as well. The proposed method has been applied on various test images and compared to the conventional BCS-OMP method. Simulation results have shown that using the proposed method has improved the quality of the output images by 2–7dB than the conventional one depending on the test image used. In addition, the computational complexity at the encoder and at the decoder for the proposed BCS-OMP technique is much less than that of the conventional technique.