Adaptive orthogonal matching pursuit and group K-SVD dictionary learning framework for bioluminescence tomography

Bioluminescence tomography (BLT) is a promising molecular imaging modality with significant potential in preclinical research, enabling three-dimensional quantitative reconstruction of internal bioluminescent sources. However, the low absorption and severe photon scattering effects in biological tissues render the BLT inverse problem highly ill-conditioned, often leading to unstable and inaccurate reconstruction results. In this study, an adaptive orthogonal matching pursuit with group K-singular value decomposition (AOMP-GKSVD) algorithm is proposed within a dictionary learning framework. An adaptive sparsity estimation mechanism is incorporated into the sparse coding phase to infer the sparsity level from the measured data and the system matrix, thereby better capturing the intrinsic sparsity characteristics of bioluminescent sources. This overcomes the limitation of fixed sparsity settings in conventional OMP, enhancing reconstruction accuracy and robustness, while saving time and effort by eliminating the need for manual sparsity tuning under varying noise and source conditions. During the dictionary update phase, a grouping strategy based on a discretized tetrahedral mesh is employed, in which atoms are updated collectively at the group level, exploiting spatial adjacency to maintain coherence and efficiently reconstruct clustered source regions. The performance of AOMP-GKSVD was validated through a series of numerical simulations and a light source implantation experiment. The experimental results demonstrate that AOMP-GKSVD achieves superior performance in terms of localization accuracy, morphological recovery, and robustness, highlighting its potential to advance the practical application of BLT in preclinical optical molecular imaging.