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Ultrasonic Nakagami images can complement conventional B-mode images for scatterer characterization. White noise in anechoic areas leads to artifacts that affect the Nakagami image to characterize tissues. Artifact removal requires rejection of the white noise without deforming the backscattered waveform. This study proposes a noise-assisted correlation algorithm (NCA) and carries out simulations, phantom experiments, and clinical measurements to validate its feasibility and practicality. The simulation results show that the NCA can reject white noise in an anechoic area without any deformation of the backscattered waveforms. The results obtained from phantoms and tissues further demonstrate that the proposed NCA can suppress a Nakagami image artifact without changing the texture of the Nakagami image of the scattering background. The NCA is an essential algorithm to construct artifact-free Nakagami image for correctly reflecting scatterer properties of biological tissues.