<p>Multi-modal medical fused images encapsulate rich pathological tissue information, offering critical support for clinical decision-making and assisted diagnosis. However, prevailing medical image fusion methodologies exhibit deficiencies in concurrently enhancing visual fidelity and preserving intrinsic energy information of tissues. For this purpose, we construct a new fusion framework of MRI and PET joint latent low rank representation with truncated Huber filtering. Under the proposed framework, feature information, low frequency parts and high frequency parts can be obtained. To effectively detect energy information of tissues in medical images, we propose a hesitant fuzzy granular energy which imitates the cognitive ability of human beings with multiple levels and perspectives. And hesitant fuzzy granular energy with fast guide filter is constructed to fuse low frequency parts. Also, we propose the directional pseudo spatial frequency to detect fine size information on oblique directions of tissues. And directional pseudo spatial frequency with dual channel PCNN is employed for fusing high frequency parts and feature information. Experimental results display that the proposed fusion method has a superior performance in visual perception, and also has advantages in a variety of evaluation metrics, by comparing with 10 state-of-the-art methods.</p>