Due to the sparse feature enhancement only concentrating on strong scatterers of target of interest, the conventional sparsity-driven synthetic aperture radar (SAR) imagery often encounters the loss of elaborated-structure features, where weak scatterers would be overlapped by the sidelobes of strong scatterers. In this article, an elaborated-structure awareness SAR (ESA-SAR) imaging algorithm is proposed based on Hessian-enhanced total variation (HETV) regularization and cooperation. By encoding the Hessian operator onto the prior of the interested target, the high-order information connected with elaborated-structure features of interests can be captured. Different from the conventional high-order formulation that is projected onto Euclidean norm balls, the proposed algorithm uses the Schatten norm balls as the projection space, where the high-order structure tensor is established, and the elaborated-structure feature can be extracted under the intended convex regularizer. More specifically, the HETV regularizer is analytically solved under the proximal algorithm considering its nondifferentiability. An eigen-soft-thresholding (E-ST) operator is derived, so that a closed-form solution for the elaborated-structure feature can be obtained. Moreover, a synergistic multitask learning framework embedded with the sparse feature enhancement is introduced, in which the elaborated-structure feature can be solved in a cooperative manner. The cooperative learning is guaranteed in terms of both theoretical and practical aspects. Finally, both simulated and raw SAR data are processed to validate the effectiveness of the ESA-SAR algorithm. Comparisons with conventional algorithms examine the superiority of the proposed algorithm.