Study on sampling matrices for far-end image reconstruction by block compressed sensing

Compressed Sensing (CS) can be used to reconstruct signals by using lesser number of samples than what is required by the Nyquist sampling rate. However, the reconstruction requires a large number of calculations. Block Compressed Sensing (BCS) reduces the computational complexity by reconstructing the signal in blocks, using the same measurement matrix for each block. BCS requires lesser memory to store the sampling matrix, and it also reduces the computational requirements at the receiver. This work studies the quality of reconstruction by transmitting the BCS measurements through a noisy channel using OFDM. Block size, sampling rate per block, channel SNR, and the type of measurement matrix are the variables that strongly affect the CS image reconstruction after reception. This work also emphasizes the importance of transmitting the BCS measurement using OFDM, and determines the better reconstruction algorithm between OMP and SPL based on the factors described above. This work proposes the use of binary sensing matrices as sampling matrix and its effect on reconstruction is also demonstrated.