Independent component analysis (ICA) is a popular approach for blind source separation (BSS). In this study, we develop a new mutual information measure for BSS and unsupervised learning of acoustic models. The underlying concept of ICA unsupervised learning algorithm is to demix the observations vectors and identify the corresponding mixture sources. These independent sources represent the specific speaker, gender, accent, noise or environment, etc, embedded in acoustic models. The novelty of the proposed ICA is to derive a new metric of mutual information for measuring the dependence among mixture sources. We focus on building this metric based on the Jensen's inequality, which is illustrated to use smaller number of iterations in finding the demixing matrix compared to other types of mutual information. We present a parametric ICA using the generalized Gaussian distribution to characterize the non-Gaussianity of model parameters. Also, a nonparametric ICA is established by using the Parzen window based distribution. In the experiments on BSS and noisy speech recognition, we demonstrate the effectiveness of the proposed Jensen ICA compared to FastICA and other nonparametric ICA.