This work presents a combined quasi-Helmholtz preconditioning strategy for the contrast source volume integral equation (J-VIE) with a Newton-Kantorovich method allowing 2D microwave imaging for high-contrast scatterers. We show that the preconditioning improves the convergence of the J-VIE, reducing the number of iterations required, even for highly inhomogeneous objects. We demonstrate the practical significance of this preconditioned inverse scattering scheme on a realistic human bone and thigh imaging problem.