Radiation-induced acoustics (RIA) shows promise in advancing radiological imaging and radiotherapy dosimetry methods. However, RIA signals often require extensive averaging to achieve reasonable signal-to-noise ratios, which increases patient radiation exposure and limits real-time applications. Therefore, this paper proposes a discrete wavelet transform (DWT) based filtering approach to denoise the RIA signals and avoid extensive averaging. The algorithm was benchmarked against low-pass filters and tested on various types of RIA sources, including low-energy X-rays, high-energy X-rays, and protons. The proposed method significantly reduced the required averages (1000 times less averaging for low-energy X-ray RIA, 32 times less averaging for high-energy X-ray RIA, and 4 times less averaging for proton RIA) and demonstrated robustness in filtering signals from different sources of radiation. The coif5 wavelet in conjunction with the sqtwolog threshold selection algorithm yielded the best results. The proposed DWT filtering method enables high-quality, automated, and robust filtering of RIA signals, with a performance similar to low-pass filtering, aiding in the clinical translation of radiation-based acoustic imaging for radiology and radiation oncology.