This image sharing method is a secure way of protecting the security of the secret images. In 2011, Wang et al. proposed an image sharing method with verification. The idea of the method is to embed the secret and the watermark images into two shares by two equations to achieve the goal of the secret sharing. However, the constructed shares are meaningless images which are difficult to manage. Authors utilize the algorithm of the torus automorphism to increase the security of the shares. However, the algorithm of the torus automorphism must take much time to encrypt and decrypt an image. This paper proposes a friendly image sharing method to improve the above problem. Experimental results show the significant efficiency of the proposed method.

In various applications of signals transmission and processing, there is always a possibility of loss of samples. The iterative algorithm of Papoulis-Gerchberg (PG) is famous for solving the band-limited lost samples recovery problem. Two problems are known in this domain: (1) a band-limited signal practically is difficult to be obtained and (2) the convergence rate is too slow. By inserting a subtraction by a polynomial in the PG algorithm, using boundary-matched concept, a significant increase in performance and speed of its convergence has been achieved. In this paper, we propose an efficient approach to restore lost samples by adding a preprocess which meets the periodic boundary conditions of Fast Fourier transform in the iteration method. The accuracy of lost samples reconstruction by using the PG algorithm can be greatly improved with the aid of mapping the input data sequence of satisfying the boundary conditions. Further, we also developed another approach that force the signal to meet a new critical boundary conditions in Fourier domain that make the parameters of the preprocessing can be easily obtained. The simulation indicates that the mean square error (MSE) of the recovery and the convergence rate with the preprocess concept is better and faster than the one without preprocess concept. Our both proposed approaches can also be applied to other cases of signal restoration, which allow Cadzow's iterative processing method, with more convenience and flexibility.