Block Compressive Sensing Based On DSS Matrix And Its Application In Digital Watermark

The Shannon/Nyquist sampling theorem specifies that to avoid losing information when capturing a signal, one must sample at least two times faster than the signal bandwidth. In many applications, including digital image and video cameras, the Nyquist rate is so high that too many samples result, making compression a necessity prior to storage or transmission. In other applications, including imaging systems (medical scanners and radars) and high-speed analog-to-digital converters, increasing the sampling rate is very expensive. Compressive sensing is an emerging theory in the field of signal processing, and it presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate. It employs nonadaptive linear projections that preserve the structure of the signal; the signal is then reconstructed from these projections using an optimization process. It reduces the cost of acquisition, storage, processing and transmission of information significantly.In general, compressive sensing is not employed to images directly as the sampling process requires to access the entire target at once and the size of measurement matrix is quite large for unprocessed images, require more memory. One skill is to divide the image into small blocks, and each block is sampled independently using the same measurement operator. Measurement matrix chosen in compressive sensing is a Gaussian i.i.d matrix or a partial random Fourier matrix, however, if so, the reconstructed image can't be obtained unless the reconstruction is done completely. A new class of dual-scale sensing matrix, can be used to generate fast preview of the reconstructed image before reconstruction, while at the same time preserving the properties that enable CS reconstruction. In this paper, we employ the key property to generate low-resolution preview first, interpolate it and then utilize the technology of projection onto convex set and hard thresholding to obtain the image with full-resolution. Compared to reconstruction by TV norm, this method appears time efficiency and high quality.Due to advancement in technology, it becomes easy to digitize text, images, videos etc. Digital data can be accessed and shared easily with the help of Internet. But this leads to rampant misuse of digital data as well. Digital watermarking serves as a solution over the above said problem. The criterion to evaluate a digital watermark process system is whether it possesses security, invisibility, validity, robustness etc. Combining compressive sensing with digital watermark, correct watermark can't be extracted if measurement matrix is not known. Not only security is completed, but also the capacity of watermark embedding is increased greatly. In this paper, a digital watermark algorithm is proposed depending on compressive sensing which is based on DSS matrix, combing with characters of human visual system. The innovation in this paper is the ability to provide two outputs, i.e. one fast low-resolution output and one high-quality CS reconstruction output which is as the same size with the original watermark image. Experiments turn out that the algorithm works well dealing with both gray-scale images and RGB images. Comparing with former digital watermarking algorithms, our algorithm behaves better robustness when suffering attacks. In addition, the algorithm shows more powerful against attacks when employed in RGB images than when employed in gray-scale images, so it has a bright application future as color images are more common nowadays.