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Ultrasound nonlinear contrast imaging using microbubble-based contrast agents has been widely investigated. However, the degree of contrast enhancement is often limited by overlap between the spectra of the tissue and microbubble nonlinear responses, which makes it difficult to separate them. The use of ensemble empirical mode decomposition (EEMD) in the Hilbert-Huang transform (HHT) was previously explored with the aim of alleviating this problem. The HHT is designed for analyzing nonlinear and nonstationary data, whereas EEMD is a method associated with the HHT that allows decomposition of data into a finite number of intrinsic mode functions (IMFs). It was found that the contrast can be effectively improved in certain IMFs, but manual selection of appropriate IMFs is still required. This prompted the present study to test the hypothesis that the contrast can be enhanced without requiring manual selection by summing appropriately weighted IMFs and demodulating the signal at appropriate frequencies. That is, a data-driven mechanism for determining weights and demodulation frequencies was derived and tested. Phantom results show that an overall contrast enhancement of up to 12.5 dB can be achieved. A fused-image representation that simultaneously displays the conventional B-mode image and the new contrast-mode image is also presented.