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This paper presents a novel formulation and consequently a new solution for two dimensional TM electromagnetic integral equations by the method of moments in polar coordination. The main idea is the reformulation of the 2-D problem according to addition theorem for Hankel functions that appear in Green function of 2-D homogeneous media. In this regard, recursive formulas in spatial frequency domain are derived and the scattering field is rewritten into inward and outward components and, then, the primary 2-D problem can be solved using 1D FFT in the stabilized biconjugate-gradient fast Fourier transform BCGS-FFT algorithm. Because the emerging method obtains 1D FFT over a circle, there is no need to expand an object region by zero padding, whereas it is necessary for conventional 2D FFT approach. Therefore, the method saves lots of memory and time over the conventional approach. other interesting aspect of the proposed method is that the field on a circle outside a scattering object, can be calculated efficiently using an analytical formula. This is, particularly, attractive in electromagnetic inverse scattering problems and microwave imaging. The numerical examples for 2-D TM problems demonstrate merits of proposed technique in terms of the accuracy and computational efficiency.

This paper presents a reversible data hiding in encrypted image (RDHEI), which divides image into non-overlapping blocks. In each block, central pixel of the block is considered as leader pixel and others as follower ones. The prediction errors between the intensity of follower pixels and leader ones are calculated and analyzed to determine a feature for block embedding capacity. This feature indicates the amount of data that can be embedded in a block. Using this pre-process for whole blocks, we vacate rooms before the encryption of the original image to achieve high embedding capacity. Also, using the features of all blocks, embedded data is extracted and the original image is perfectly reconstructed at the decoding phase. In effect, comparing to existent RDHEI algorithms, embedding capacity is significantly increased in the proposed algorithm. Experimental results confirm that the proposed algorithm outperforms state of the art ones.