Acoustic clutter produced by off-axis and multipath scattering is known to cause image degradation, and in some cases these sources may be the prime determinants of in vivo image quality. We have previously shown some success addressing these sources of image degradation by modeling the aperture domain signal from different sources of clutter, and then decomposing aperture domain data using the modeled sources. Our previous model had some shortcomings including model mismatch and failure to recover B-Mode speckle statistics. These shortcomings are addressed here by developing a better model and by using a general regularization approach appropriate for the model and data. We present results with L1 (lasso), L2 (ridge), and L1/L2 combined (elastic-net) regularization methods. We call our new method aperture domain model image reconstruction (ADMIRE). Our results demonstrate that ADMIRE with L1 regularization, or weighted toward L1 in the case of elastic-net regularization, have improved image quality. L1 by itself works well, but additional improvements are seen with elastic-net regularization over the pure L1 constraint. On in vivo example cases, L1 regularization showed mean contrast improvements of 4.6 and 6.8 dB on fundamental and harmonic images, respectively. Elastic net regularization (α = 0.9) showed mean contrast improvements of 17.8 dB on fundamental images and 11.8 dB on harmonic images. We also demonstrate that in uncluttered Field II simulations the decluttering algorithm produces the same contrast, contrast-tonoise ratio, and speckle SNR as normal B-mode imaging, demonstrating that ADMIRE preserves typical image features.