SPARSE ANALYSIS MODEL BASED DICTIONARY LEARNING FOR SIGNAL DECLIPPING

Clipping is a common type of distortion in which the amplitude of a signal is truncated if it exceeds a certain threshold. Sparse representation has underpinned several algorithms developed recently for reconstruction of the original signal from clipped observations. However, these declipping algorithms are often built on a synthesis model, where the signal is represented by a dictionary weighted by sparse coding coefficients. In contrast to these works, we propose a sparse analysis-model-based declipping (SAD) method, where the declipping model is formulated on an analysis (i.e. transform) dictionary, and additional constraints characterizing the clipping process. The analysis dictionary is updated using the Analysis SimCO algorithm, and the signal is recovered by using a least-squares based method or a projected gradient descent method, incorporating the observable signal set. Numerical experiments on speech and music are used to demonstrate improved performance in signal to distortion ratio (SDR) compared to recent state-of-the-art methods including A-SPADE and ConsDL