Non-iterative Pseudo Inverse Based Recovery Algorithm (NIPIRA) for Compressively Sensed Images and Videos

Recent development in data compression emphasizes compressed sensing technique as a widely applied one for compression and reconstruction of images and videos by projecting the pixel values into smaller dimensional measurements. These compressed measurements are reconstructed at the receiver using suitable reconstruction algorithms, generally the greedy algorithms. Greedy algorithms are time consuming and complex processes, giving rise to a trade-off between reconstruction performance and algorithmic performance. This work proposes a non-iterative method, non-iterative pseudo inverse based recovery algorithm (NIPIRA), for reconstruction of compressively sensed images and videos that exhibits small complexity and time requirement along with preservation of reconstruction quality. Mathematical proofs for NIPIRA’s accuracy and optimality provide additional theoretical support to the algorithm. NIPIRA gives a minimum PSNR of 32 dB for very few measurements, accuracy of above 97 and 92% decrease in elapsed time compared with other iterative algorithms. The complexity of NIPIRA is \(O(MN)\) which is \(s\) times less than OMP and StOMP.