A compressive sensing based on watermarking scheme for sparse image

The traditional Nyquist Shannon theorem explains that the number of samples which are needed for recovering a signal must be at least twice the maximum frequency in the bandwidth of a signal. This approach is used in all applications of the signal processing. This problem is solved by using a new sampling method developed called Compressive Sampling or Compressive Sensing (CS), where it is used to recover signals or images from far fewer measurements or samples than the traditional theorem. CS theory depends on Sparsity principle, thereby the signals or images must be sparse. However, most of the natural signals or images are not sparse. Therefore, there are some transformation methods used to alter these signals or images into sparse like Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT) and Discrete Fourier Transform (DFT). In this thesis, we integrate the watermarking technology and compressive sensing theory to protect the watermarking image in the compressive sensing measurements. The watermarking image is embedded into the compressive measurement vectors. The measurement vectors are sparse in a suitable basis. The resulting watermarked measurements recover by using both the Orthogonal Matching Pursuit (OMP) and Orthogonal Matching Pursuit With Partially Known Support (OMP-PKS) reconstruction algorithms. Then the decoder procedure utilizes to extract the watermarking image. In experimental study, the results obtained by comparing between the OMP and OMP-PKS algorithms to clarify the performance of them. The results show that the OMP-PKS algorithm achieves performance superior to that of the OMP reconstruction algorithm.