Due to the fact that natural images are approximately sparse in Discrete Cosine Transform (DCT) or wavelet basis, the Compressive Sensing (CS) can be employed to decode both the host image and watermark with zero error, despite not knowing the host image. In this paper, Limited-Random Sequence (LRS) matrix is utilized to implement the blind CS detection, which benefits from zero error and lower complexity. The performance in Bit Error Rate (BER) and error-free detection probability confirms the validity and efficiency of the proposed scheme.

Limited Random Sequence (LRS) is quite important for Analog-to-Information Converter (AIC) because it determines the random sampling scheme and the resultant performance. LRS is established with the elements of “0” and “1”. The “1” appears randomly in the segment of the sequence, so that the production of the original signal and LRS can be considered as the approximation of the random sampling of the original signal. The random sampling result can perfectly recover the signal with Compressive Sensing (CS) algorithm. In this paper, a high order LRS is proposed for the AIC design in Distributed Compressive Sensing (DCS), which has the following three typical features: 1) The high order LRS has the elements of integer which can indicate the index number of the sensor in DCS. 2) High order LRS can adapt to the sparsity variation of the original signal detected by each sensor. 3) Employing the AIC with high order LRS, the DCS algorithm can recover the signal with very low sampling rate, usually above 2 orders less than the traditional distributed sensors. In the paper, the scheme and the construction algorithm of high order LRS are proposed. The performance is evaluated with the application studies of the distributed sensor network and the camera picture correspondingly.