Microwave imaging (MWI) is a diagnostic tool whose working principle relies on the dielectric contrast between lesions and healthy tissues, and could be used, for instance, to detect breast cancer or brain strokes. This work aims to improve the speed of the processing of MWI data acquired when using a finite element contrast source inversion method. The processing consists of solving a large sparse and complex linear system with 24 right-hand sides. Multiple open-source solvers (UMFPACK, KLU, Eigen and MUMPS) were tested to solve this linear system, including direct and indirect methods, and the precision obtained from each trial was compared.