With the accomplishment of the Human Genome Project, the significance of protein structure research becomes more outstanding. The prediction of protein structure is aimed at the study of amino acid molecules, and belongs to the field of Bio-Nano research. There are two kinds of methods to study protein structure: experiment and theory. This paper adopts ab-initio prediction method which is one of theoretical methods. Based on the "thermodynamic hypothesis," there are many different models applied to the field. This paper selects 3D AB off-lattice model to solve this problem. ABC-PIO combines the characteristics of the diversity generated by artificial bee colony algorithm and the fast convergence speed of pigeon inspired optimization. At the end of this algorithm, Cauchy perturbation strategy is added to optimize the local optimum. Two functions are introduced to dynamically control two operators of the hybrid algorithm. In order to test the quality of ABC-PIO, ten real protein sequences from the Protein Data Bank have been selected. Compared with other four algorithms, the algorithm gets better result. To calculate the error between the predicted and the true protein structure RMSD is set. Comparisons are made not only in the convergence curves but also in the backbone drawings.

Magnetic resonance imaging (MRI) faces ongoing challenges associated with prolonged acquisition times and susceptibility to motion artifacts. Compressed Sensing (CS) principles have emerged as a significant advancement, addressing these issues by subsampling k-space data points and enabling rapid imaging. Nevertheless, the recovery of intricate details from under-sampled data remains a complex endeavor. In this study, we introduce an innovative deep learning approach tailored to the restoration of high-fidelity MRI images from under-sampled k-space data. Our method employs a cascaded reconstruction strategy that progressively restores hierarchical features and fuses them to achieve the final reconstruction. This cascade encompasses low, intermediate, and high orders of reconstruction, which is followed by a return through intermediate and low orders. At distinct reconstruction stages, we introduce a novel reconstruction block to recapture diverse frequency information crucial for image reconstruction. The other core innovation of our proposal lies in a fusion algorithm that harmonizes results from various reconstruction tiers into the final MRI image. Our methodology is validated using two distinct datasets. Notably, our algorithm achieves impressive PSNR values of 32.60 and 31.02 at acceleration factors of 4× and 8× in the FastMRI dataset along with SSIM scores of 0.818 and 0.771, outperforming current state-of-the-art algorithms. Similarly, on the Calgary–Campinas dataset, our algorithm achieves even higher PSNR values, reaching 37.68 and 33.44, which is accompanied by substantial SSIM scores of 0.954 and 0.901. It is essential to highlight that our algorithm achieves these remarkable results with a relatively lower parameter count, underscoring its efficiency. Comparative analyses against analogous methods further emphasize the superior performance of our approach, providing robust evidence of its effectiveness.