Construction of compressed sensing matrixes based on the singular pseudo-symplectic space over finite fields

Compressed sensing（CS） provides a new approach to acquire data as a sampling technique and makes it sure that a sparse signal can be reconstructed from few measurements. The construction of compressed matrixes is a central problem in compressed sensing. This paper provides a construction of deterministic CS matrixes, which are also disjunct and inclusive matrixes, from singular pseudo-symplectic space over finite fields of characteristic 2. Our construction is superior to De Vore＇s construction under some conditions and can be used to reconstruct sparse signals through an efficient algorithm.

Construction of deterministic sensing matrix and its application to DOA estimation

Compressive sensing（CS） has emerged as a novel sampling framework which enables sparse signal acquisition and reconstruction with fewer measurements below the Nyquist rate.An important issue for CS is the construction of measurement matrix or sensing matrix.A new deterministic sensing matrix,named as OOC-B,is proposed by exploiting optical orthogonal codes（OOCs）,Bernoulli matrix and Singer structure,which has the entries of 0,＋1 and-1 before normalization.We have proven that the designed deterministic matrix is asymptotically optimal.In addition,the proposed deterministic sensing matrix is applied to direction of arrival（DOA） estimation of narrowband signals by CS arrays（CSA）processing and CS recovery.Theoretical analysis and simulation results show that the proposed sensing matrix has good performance for DOA estimation.It is very effective for simplifying hardware structure and decreasing computational complexity in DOA estimation by CSA processing.Besides,lower root mean square error（RMSE） and bias are obtained in DOA estimation by CS recovery.

Robust signal recovery algorithm for structured perturbation compressive sensing

It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.

Optical SDMA for applying compressive sensing in WSN

In order to apply compressive sensing in wireless sensor network, inside the nodes cluster classified by the spatial correlation, we propose that a cluster head adopts free space optical communication with space division multiple access, and a sensor node uses a modulating retro-reflector for communication. Thus while a random sampling matrix is used to guide the establishment of links between head cluster and sensor nodes, the random linear projection is accomplished. To establish multiple links at the same time, an optical space division multiple access antenna is designed. It works in fixed beams switching mode and consists of optic lens with a large field of view（FOV）, fiber array on the focal plane which is used to realize virtual channels segmentation, direction of arrival sensor, optical matrix switch and controller. Based on the angles of nodes＇ laser beams, by dynamically changing the route, optical matrix switch actualizes the multi-beam full duplex tracking receiving and transmission. Due to the structure of fiber array, there will be several fade zones both in the focal plane and in lens＇ FOV. In order to lower the impact of fade zones and harmonize multibeam, a fiber array adjustment is designed. By theoretical, simulated and experimental study, the antenna＇s qualitative feasibility is validated.

A Verifiable Secret Image Sharing Scheme Based on Compressive Sensing

This paper proposes a verifiable secret image sharing scheme based on compressive sensing, secret sharing, and image hashing. In this scheme, Toeplitz matrix generated by two chaotic maps is employed as measurement matrix. With the help of Shamir threshold scheme and image hashing, the receivers can obtain the stored values and the hash value of image. In the verifying stage and restoring stage, there must be at least t legal receivers to get the effective information. By comparing the hash value of the restored image with the hash value of original image, the scheme can effectively prevent the attacker from tampering or forging the shared images. Experimental results show that the proposed scheme has good recovery performance, can effectively reduce space, and is suitable for real-time transmission, storage, and verification.