A Novel Fast and Efficient BEMD for Large Images Using the Partition of Unity Method and Compactly Supported RBFs

In this paper, we present a fast and effective method for Bidimensional Empirical Mode Decomposition (BEMD) of large images. The proposed approach is based on the integration and adaptation of the partition of unity (PU) algorithm with compactly supported radial basis functions (CSRBFs) within the BEMD method. While the traditional BEMD algorithm is computationally intensive due to its reliance on envelope interpolation, the novel approach overcomes this limitation, as demonstrated by both complexity analysis and experimental results. Results obtained from both synthetic and real images demonstrate significant improvements in computational efficiency and decomposition quality compared to the recent BEMD-CSRBF approach, which demonstrates an important advancement over traditional BEMD methods. These improvements are reflected in lower orthogonality index (OI) values and faster processing times compared to the BEMD-CSRBF method. Across the tested images, the proposed BEMD-PU method reduces the computation time by (17.22%)–(69.94%) and decreases the OI by (8.93%)–(62.23%) compared with BEMD-CSRBF; on average, the computation time and OI are reduced by (44.76%) and (31.49%), respectively. Consequently, the proposed method performs exceptionally well with large images, making it an efficient tool for image processing.