When using ultrasound to image heterogeneous media, echoes from multiple and off-axis scattering can overwrite the recorded ballistic wavefronts of interest. This reduces the coherence of signals across the aperture and causes clutter in the final image. Therefore, separating those unwanted events from the signal of interest is necessary to improve the visibility of structures in a B-mode image, and also to enable other processing methods that require coherent channel signals, such as various phase-aberration-correction techniques and sound-speed estimators. We used prediction-error filters (PEFs) to model the signal and the assumed additive noise in the data acquired through a 10 mm thick layer of beef tissue placed above a speckle region of a phantom. The PEF coefficients used to model the signal were first computed from the phantom data collected without tissue and subsequently employed to deconvolve the tissue data and find the PEF associated with the noise. These two filters were then used in a joint-inversion framework to separate the signal and noise components recorded within the original tissue data. In order to be able to apply our method in scenarios where direct measurements of the signal proxy are not available, we also evaluated the signal-PEF coefficients from the theoretical model of the signal from diffuse targets as provided by the van-Cittert Zernike (VCZ) theorem. To evaluate the quality of the separation of signal from the noise, we compared the original channel data acquired through the tissue with its estimated ballistic-wave component, as well as their corresponding spectra. We also compared performance of the proposed technique to F-X filter, which is a popular linear-predictionbased filter used to suppress noise in channel data. After the removal of acoustic noise from the channel data, coherence across the aperture increases. The average nearest-neighbor cross-correlation computed on the original data is 0.47, while the nearest-neighbor cross-correlation of the estimated ballistic-wave component is 0.81 or 0.97, depending whether the experimental or theoretical signal-PEFs are used in the estimation process.