Magnetic resonance imaging is mostly employed in medicine for disease diagnosis. In medical image analysis, brain tumor segmentation includes separating brain tumors from healthy regions in MRI data. Using dynamic MRI scans, machine learning is employed to separate background and foreground elements. Convex optimization models such as RPCA, WSNM, and WNNM can be used for estimating low rank and sparse components, but they provide biased results. Non-convex optimization was proposed to overcome the drawbacks of convex optimization. Non-convex relaxation such as Composite Regularized (Co-Re), Adaptive Composite Regularized Low-Rank plus Sparse Decomposition (Ada Co-Re LSD) Type 1 and Type 2 provides more accurate results compared to convex relaxation. It separates the background and foreground of an image accurately and takes less time to complete the process. Non-convex methods could interpret the dynamically changing background as target objects in the foreground, creating issues with selective and empty edge recognition. In order to overcome this challenge, Adaptive non-convex rank approximation along with superpixel segmentation techniques are proposed in this paper. First, the brain MRI video sequence’s super pixels are marked, and the super pixel grouping matrix is obtained using the linear spectral clustering (LSC) segmentation approach. With the Otsu algorithm, the motion mask matrix is generated. The performance metrics such as PSNR, F-measure, AGE, Peps and Accuracy are evaluated for non-convex algorithms with superpixel segmentation techniques. Ada Co-Re LSD Type 2 with LSC superpixel segmentation technique performed more effectively compared to other algorithms in separating the tumor part under complex dynamic background words.