In this paper, both global exponential stability and periodic solutions are investigated for a class of delayed reaction-diffusion BAM neural networks with Dirichlet boundary conditions. By employing suitable Lyapunov functionals, sufficient conditions of the global exponential stability and the existence of periodic solutions are established for reaction-diffusion BAM neural networks with mixed time delays and Dirichlet boundary conditions. The derived criteria extend and improve previous results in the literature. A numerical example is given to show the effectiveness of the obtained results.

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Sheared beam imaging (SBI) is considered a computational imaging technique that transmitted three sheared coherent laser beamlets for illumination, and a sensor array to receive the intensity of speckle pattern reflected from the target. SBI can be used to image remote objects through a turbulent medium without the need for any adaptive optics. However, while imaging low-orbit moving targets, the number of detectors of sensor array required for the receiving system of SBI are very large, and the development of sensor array is difficult and costly. This paper proposes the spatial domain sparse sampling technique for the SBI system through transmitting five laser beamlets to illuminate the target carrying more of its spectral information, which can reduce the number of detectors of the sensor array. Firstly, the principle of the sparse imaging technique is deduced. Then, a sparse reconstruction algorithm is studied. The phase difference and amplitude information of the target in the echo signal after sparse sampling can be extracted accurately by searching for the accurate positions of the beat frequency components. The wavefront phases can be demodulated by the least-squares method, and wavefront amplitude can be obtained by the algebraic operation of speckle amplitude. The reconstructed wavefront is used to formulate the two-dimension image of the target. Theoretically, without affecting the resolution, the number of detectors of the sensor array can be reduced to half of the traditional three-beam method, which breaks through the limitation that the detector spacing of sensor array is equal to the shear lengths of beamlet. From simulation results, when the number of detectors of the sensor array is reduced by fifty percent, the proposed sparse reconstruction algorithm has almost the same quality as the reconstructed image with the traditional three-beam method.

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