Latent Low-Rank Representation (LatLRR) has emerged as a prominent approach for fusing visible and infrared images. In this approach, images are decomposed into three fundamental components: the base part, salient part, and sparse part. The aim is to blend the base and salient features to reconstruct images accurately. However, existing methods often focus more on combining the base and salient parts, neglecting the importance of the sparse component, whereas we advocate for the comprehensive inclusion of all three parts generated from LatLRR image decomposition into the image fusion process, a novel proposition introduced in this study. Moreover, the effective integration of Convolutional Neural Network (CNN) technology with LatLRR remains challenging, particularly after the inclusion of sparse parts. This study utilizes fusion strategies involving weighted average, summation, VGG19, and ResNet50 in various combinations to analyze the fusion performance following the introduction of sparse parts. The research findings show a significant enhancement in fusion performance achieved through the inclusion of sparse parts in the fusion process. The suggested fusion strategy involves employing deep learning techniques for fusing both base parts and sparse parts while utilizing a summation strategy for the fusion of salient parts. The findings improve the performance of LatLRR-based methods and offer valuable insights for enhancement, leading to advancements in the field of image fusion.