This paper presents a phase retrieval algorithm that incorporates sparsity priors into total variation and framelet regularization. The proposed algorithm exploits the sparsity priors in both the gradient domain and the spatial distribution domain to impose desirable characteristics on the reconstructed image. We utilize structured illuminated patterns in holography, consisting of three light fields. The theoretical and numerical analyses demonstrate that when the illumination pattern parameters are non-integers, the three diffracted data sets are sufficient for image restoration. The proposed model is solved using the alternating direction multiplier method. The numerical experiments confirm the theoretical findings of the lighting mode settings, and the algorithm effectively recovers the object from Gaussian and salt–pepper noise.

In order to improve the high-precision tracking control of angle variables and the sliding mode equivalent control part for the 3-RRS parallel manipulator, an adaptive neural network fuzzy sliding mode control algorithm with self-adjusting switching gain is proposed. Firstly, considering the uncertainty of the constrained force between derived links and the moving platform, the complete dynamic model including ideal and non-ideal constrained force is established by combining with the Udwadia-Kalaba(U-K) equation and Lagrange method. Secondly, the neural network sliding mode controller is designed to realize the approximate solution of the sliding mode equivalent control part. At the same time, in order to reduce the chattering phenomenon of the neural network sliding mode controller, a fuzzy adjustment rule of switching gain is designed to better compensate for the uncertain terms. And then the stability of the control system is proved by the Lyapunov method. Finally, the proposed control algorithm is simulated on the 3-RRS parallel manipulator. The simulation results show that the chattering phenomenon is overcome. The high-precision control of angle variables and the sliding mode equivalent control part is realized.

In order to achieve high precision control of the dexterous hand, an adaptive neural network sliding mode control algorithm based on the U-K (Udwadia-Kalaba) equation is proposed. Firstly, based on the U-K equation and considering the ideal and non-ideal constrained force at each link of the dexterous hand, the detailed dynamic equation is derived. Secondly, considering the uncertainty of the non-ideal constrained force (mainly the friction force on each link of the dexterous hand) and the chattering phenomenon when using sliding mode control alone, the adaptive neural network and the sliding mode control algorithm are combined to realize the high-precision tracking and estimation of each link angle trajectory and the non-ideal constrained force. Finally, in order to verify the correctness and rationality of the proposed algorithm, the 3-DOF spatial dexterous hand is taken as the simulated object. The simulation results show that the tracking and estimation errors of each link angle and the non-ideal constrained force are 10⁻² order of magnitude.