Sparsity Measures-Enhanced Targeted Diffusion Probabilistic Model for Acoustic Signal Recovery

Recovering target data from measured signals distorted by non-Gaussian noise in inverse problems poses a persistent challenge in acoustic signal processing, especially within industrial scenarios. This study addresses this challenge by introducing a novel sparsity measures-enhanced targeted diffusion probabilistic model (SMTD). Particularly, analytical formulations of the forward process are given where measured acoustic signals are incorporated as the diffusion target while sparsity measures and evidence lower bound (ELBO) are integrated into the model as the condition during the forward process. For the reverse process, a parameterized score function is introduced, conditioned on target signals. This facilitates the recovery of acoustic signals from distorted ones through a scheduled sampling strategy. Numerical results indicate that this method boosted the performance of state-of-the-art studies in the quality of recovered data. Experimental studies confirm the effectiveness in counteracting distortion caused by surrounding noise that may exist in industrial condition diagnosis scenarios and it is well-documented to apply this method to industrial condition detection to reduce the impact of surrounding noise.