Image Reconstruction via Compressed Sensing

Compressed Sensing (CS) emerged as a signal processing technique to reconstruct a signal sampled below the Nyquist sampling rate. We reconstruct a number of commonly used images using the compressed sensing method in this paper. We exploit the sparse nature of the images and reconstruct those using very few measurements. As a requirement, we have regarded the signal to be sparse either in its original domain or in some other domain. In this paper, we also experimented image reconstruction employing the compressed sensing techniques with the aid of either discrete wavelet transform (DWT) or the discrete cosine transform (DCT). We employ the basis pursuit algorithm and the Douglas-Rachford iterative algorithm for reconstructing the images. Basic theoretical and mathematical concepts underlying compressed sensing are applied. We further compare the reconstruction of the images using some well-known image quality metrics.