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This paper describes the joint use of the expectation maximization method (EM) and high resolution atomic decomposition (HRAD) to estimate the signals forming a linear mixture. HRAD overcomes the limitation in resolution of the conventional atomic decomposition, and is utilized as the initial estimate for EM. EM with HRAD outperforms other existing methods, such as single HRAD, conventional AD, and conventional AD plus EM. The Cramer-Rao Bound is used as a benchmark in the comparison, and shows the efficiency of the suggested method for high signal-to-noise ratio. The signals are modeled as chirplets.