Transcranial Doppler ultrasound imaging is a crucial tool for both clinical and research applications. Despite its significance, its utility is constrained by the dynamic range limitations of the receiver system. Traditional methods, relying on high-dynamic-range front-end amplifiers and high-resolution ADCs, are often inefficient. These methods expend unnecessary effort on the clutter component of the input signal, which, although non-targeted, dominates the signal swing. This research addresses this challenge by introducing a feedback path near the transducer end. This integration effectively mitigates the clutter component, thus relaxing the dynamic range requirements of the receiver chain. To ensure stability and precision, the system uses a closed-loop configuration with a slow-time integrator, ensuring consistent tracking of the feedback path. Simulation results underscore the system's efficiency, with a power consumption of 20.72mW and a dynamic range of 89.57dB.