Robust watermarking of compressive sensed measurements under noise attacks

Traditional methods in data acquisition follow Shannon /Nyquist sampling theo- rem; one must sample a band-limited signal by at least two times faster than the signal bandwidth to exactly reconstruct the signal. However, signals that we encounter in many applications are sparse in some proper bases, and they can be represented by very few coefficients. Therefore, the number of samples obtained in Shannon/Nyquist framework is much more than it is required to reconstruct the signal. Compressive Sensing (CS) shows that certain signals can be captured from far fewer samples as compared to conventional methods, and they can be reconstructed by developing effec- tive non-linear reconstruction algorithms. The methods of data embedding and data hiding (watermarking) for signal that is sampled based on Shannon /Nyquist sampling theorem is well advanced. However, watermarking methods for compressive sensing measurements is investigating in this thesis. The measurements that is sampled using CS methods, which is superiors to traditional methods, are required to be transmitted or stored. In addition to efficiently transmitting or storing CS-based measurements, one may wish to embed a watermark onto these measurements. Hence, the copyright information or meta-data can be embedded onto CS measurements. Such a water- marking scheme must satisfy the following properties: (i) the watermark information must be decoded exactly, and (ii) the reconstruction of the signal must not suffer at the decoder side. In this work, we propose a watermark algorithm that embeds infor- mation directly onto Compressive Sensed Measurements of a sparse signal. Proposed watermarking algorithm outperforms the classical l2 and l1 minimization algorithms in terms of watermark embedding capacity. Experimental results show that the proposed algorithm has a robust reconstruction performance under Gaussian and impulsive noise.