A comparative study of spike and smooth separation from a signal using different overcomplete dictionary

Most of the natural signals are complex and are highly time varying, since they are non stationary in nature. In this paper, a comparative study for separating spikes and smooth signal components from a non-stationary signal are performed based on different overcomplete dictionaries. The experiment is evaluated using the sparse representation with different bases such as the Discrete Cosine Transform (DCT), Walsh-Hadamard, Orthogonal and Biorthogonal wavelet basis. The primary focus of this paper is to use L₁ minimization for retrieving the smooth and spikes component of the signal using different overcomplete dictionary. The experimental results reveals out the dictionary that delivers a better separation without distorting temporal and spectral characteristics.