A fast reconstruction algorithm for bioluminescence tomography based on smoothed l0 norm regularization

As an important optical molecular imaging technique, bioluminescence tomography (BLT) offers an inexpensive and sensitive means for non-invasively imaging a variety of physiological and pathological activities at cellular and molecular levels in living small animals. The key problem of BLT is to recover the distribution of the internal bioluminescence sources from limited measurements on the surface. Considering the sparsity of the light source distribution, we directly formulate the inverse problem of BLT into an l 0 -norm minimization model and present a smoothed l 0 -norm (SL0) based reconstruction algorithm. By approximating the discontinuous l0 norm with a suitable continuous function, the SL0 norm method solves the problem of intractable computational load of the minimal l 0 search as well as high sensitivity of l 0 -norm to noise. Numerical experiments on a mouse atlas demonstrate that the proposed SL0 norm based reconstruction method can obtain whole domain reconstruction without any a priori knowledge of the source permissible region, yielding almost the same reconstruction results to those of l 1 norm methods.