This paper describes the development of a reduced forward operator for solving acoustic scattering problems that arise in ultrasonic imaging applications. The reduction, inspired by the contrast source inversion technique, is obtained by decoupling the interaction between locations in the computational domain at which contrast is present and those positions at which there is a zero contrast. The decoupling is achieved by multiplication by a diagonal matrix whose entries reflect the presence or absence of contrast at the associated point. Numerical results confirm that the reduced operator produces convergent results in less iterations.