A method to remove the scattered background from a reconstructed image by deconvolution with a point response function which includes the scatter contribution is presented. The amplitude of the scattered response function is obtained by constraining a region of the corrected image to zero average amplitude. This method assumes that the shape of scatter distribution is shift invariant and independent of the shape of the scattering object and the distribution of the positron activity. The validity of these approximations for the QPET geometry was tested using simulations. An average scatter response function for the system was obtained from these simulations and compared with results from measurements. The method was tested using experimental data from an irregularly shaped acrylic phantom. It was simple to implement and resulted in a satisfactory correction of the scattered background for a small-volume system.