Clutter produced using bright acoustic sources can obscure weaker acoustic targets, degrading the quality of the image in scenarios with high dynamic ranges. Many adaptive beamformers seek to improve image quality by reducing these sidelobe artifacts, generating a boost in contrast ratio or contrast-to-noise ratio. However, some of these beamformers inadvertently introduce a dark region artifact in place of the strong clutter, a situation that occurs when both clutter and the underlying signal of interest are removed. We introduce the iterative aperture domain model image reconstruction (iADMIRE) method that is designed to reduce clutter while preserving the underlying signal. We compare the contrast ratio dynamic range (CRDR) of iADMIRE to several other adaptive beamformers plus delay-and-sum (DAS) to quantify the accuracy and reliability of the reported measured contrast for each beamformer over a wide range of contrast levels. We also compare all beamformers in the presence of bright targets ranging from 40 to 120 dB to observe the presence of sidelobes. In cases with no added reverberation clutter, iADMIRE had a CRDR of 75.6 dB when compared with the next best method DAS with 60.8 dB. iADMIRE also demonstrated the best performance for levels of reverberation clutter up to 0-dB signal-to-clutter ratio. Finally, iADMIRE restored underlying speckle signal in dark artifact regions while suppressing sidelobes in bright target cases up to 100 dB.