A transformation model based on dual-tree complex wavelet transform for non-rigid registration of 3D MRI images

Image registration is regarded as an important component of medical procedures. The present study aimed to introduce a new transformation model based on dual-tree complex wavelet transform (DT-CWT). To this aim, parametric registration methods was revised based on the function expansion theory and the gradient descent algorithm was used to introduce a general formulation for transformation models based on spatio-spectral transforms. Then, the performance of the proposed method was evaluated on a public dataset of 3D real magnetic resonance images (MRI) and compared with the transformation model based on wavelets. Finally, the performance of the proposed method was compared with the current state-of-the-art methods (IRTK, SyN and SPM-DARTEL). Based on the experimental results, the proposed method could deliver superior registration performance compared with the previous methods.

An extended Green-Sasao hierarchy of canonical ternary Galois forms and Universal Logic Modules

A new extended Green-Sasao hierarchy of families and forms with a new sub-family for many-valued Reed-Muller logic is introduced. Recently, two families of binary canonical Reed-Muller forms, called Inclusive Forms (IFs) and Generalized Inclusive Forms (GIFs) have been proposed, where the second family was the first to include all minimum Exclusive Sum-Of-Products (ESOPs). In this paper, we propose, analogously to the binary case, two general families of canonical ternary Reed-Muller forms, called Ternary Inclusive Forms (TIFs) and their generalization of Ternary Generalized Inclusive Forms (TGIFs), where the second family includes minimum Galois Field Sum-Of-Products (GFSOPs) over ternary Galois field GF(3). One of the basic motivations in this work is the application of these TIFs and TGIFs to find the minimum GFSOP for many-valued input-output functions within logic synthesis, where a GFSOP minimizer based on IF polarity can be used to minimize the many-valued GFSOP expression for any given function. The realization of the presented S/D trees using Universal Logic Modules (ULMs) is also introduced, whereULMs are complete systems that can implement all possible logic functions utilizing the corresponding S/D expansions of many-valued Shannon and Davio spectral transforms.