The paper discusses the development of algorithms for data-driven learning of domain-specific overcomplete dictionaries to achieve maximum likelihood and maximum a posteriori dictionary estimates using Bayesian models with concave/Schur-concave (CSC) negative log priors. These priors are suitable for obtaining sparse representations of environmental signals within an appropriately chosen dictionary. The elements of the dictionary can be interpreted as concepts, features, or words that succinctly express events encountered in the environment. The algorithms iteratively update the dictionary using sparse representations found by variants of the FOCUS algorithm. Experiments using synthetic data and natural images demonstrate improved performance over other independent component analysis (ICA) methods in terms of signal-to-noise ratios of separated sources. In the overcomplete case, the true underlying dictionary and sparse sources can be accurately recovered. Overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries in natural image tests.The paper discusses the development of algorithms for data-driven learning of domain-specific overcomplete dictionaries to achieve maximum likelihood and maximum a posteriori dictionary estimates using Bayesian models with concave/Schur-concave (CSC) negative log priors. These priors are suitable for obtaining sparse representations of environmental signals within an appropriately chosen dictionary. The elements of the dictionary can be interpreted as concepts, features, or words that succinctly express events encountered in the environment. The algorithms iteratively update the dictionary using sparse representations found by variants of the FOCUS algorithm. Experiments using synthetic data and natural images demonstrate improved performance over other independent component analysis (ICA) methods in terms of signal-to-noise ratios of separated sources. In the overcomplete case, the true underlying dictionary and sparse sources can be accurately recovered. Overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries in natural image tests.