Background - Ultrasound is a useful medical imaging tool. An ultrasound Image is commonly formed using Delay-and-Sum (DAS) beamforming with fixed weighting. The main disadvantages of this method, however, are wide main-lobe and significant side-lobes, which lead to low resolution and contrast of the Image. In particular, a strong reflector located next to weaker reflectors will obscure the weak reflectors. Methods - Since a typical dynamic range of ultrasound imaging is 60 dB while the DAS beamformer ideally suppresses side-lobes by only 23 dB, we propose splitting the data into two separate images using a sparsity-prior for the strong reflectors. We introduce an algorithm for locating the strong reflectors and separating them out, for the case that all the weaker reflectors are confined by the transmission beam to a relatively small area in the proximity of strong reflectors, and where the impulse response of the transducer is known. Results - Based on 10,000 in-silico simulations we show that the location and reflectivity of a sole randomly located strong reflector is extracted with good accuracy for a reflectivity value between 13dB and 33dB higher than its environment. We further show that the overall image fidelity strongly depends on precision of the detection (both position and reflectivity) of the strong reflectors. It is demonstrated that after subtracting the contribution of the strong reflector, the reflectivity function of the weaker reflectors is faithfully recovered. Conclusion – Our results show that the proposed model-based approach to ultrasound imaging can significantly improve the image quality.