Group sparse approaches to regression modeling are finding ever increasing utility in an array of application areas. While group sparsity can help assess certain data structures, it is desirable in many instances to also capture element-wise sparsity. Recent work exploring the latter has been conducted in the context of l2/l1 penalized regression in the form of the sparse group lasso (SGL). Here, we present a novel model, called the sparse group elastic net (SGEN), which uses an

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... d penalty. We show that the l∞-norm, which induces group sparsity is particularly effective in the presence of noisy data. We solve the SGEN model using a coordinate descent-based procedure and compare its performance to the SGL and related methods in the context of hyperspectral imaging in the presence of noisy observations. Supplementary materials for this article are available online.