The problem of noise removal in low signal-to-noise ratio (SNR) conditions poses a serious issue in numerous sensor-based monitoring and critical engineering applications, including aerospace systems, manufacturing processes, and infrastructure monitoring, where signals are contaminated by Gaussian and burst noise at the same time. Conventional denoising algorithms, including Wiener filter and wavelet shrinkage methods, generally apply a unified denoising approach throughout the whole signal. Thus, such algorithms frequently face challenges in obtaining a good trade-off between successful noise removal and retention of significant features of a signal, particularly under the influence of non-uniform noise types. To solve this problem, this paper presents a new adaptive framework based on a locally estimated SNR value, a mask of boundaries, and logistic fusion of wavelet-based and Wiener filtering approaches to achieve a more efficient denoising process. First, a local SNR value is calculated in order to analyze the noise variance in space. Subsequently, a soft boundary mask is created by applying a percentile-based threshold to the local SNR values and using a logistic function to distinguish between noise-dominant areas and signal-dominant areas. Finally, combining the obtained knowledge about signal and noise-dominant areas, the wavelet-based approach and the Wiener algorithm are fused in terms of weights using logistic functions. The performance of the presented framework is examined by conducting tests on synthetic signals as well as ECG recordings, which have been distorted by Gaussian and burst noises at input SNR values of -10 dB, -5 dB, and 0 dB. From the experimental results, performance enhancement can be consistently observed from the proposed technique, and the corresponding absolute output SNR values obtained are 0.69 dB, 1.10 dB, and 2.24 dB, respectively. The aforementioned results suggest that the proposed algorithm performs well with regards to both noise suppression and feature retention.