The Iterative Shrinkage Thresholding Algorithm (ISTA) is usually unfolded into a deep neural network (DNN) in compressive sensing (CS). However, existing ISTA-based unfolded algorithms concentrate on the predetermined threshold to regulate the level of sparsity, making the selection of the appropriate metric for different signals a challenging task. Especially in highly redundant signals, high-frequency components in a signal will be compromised when set to zero after the application of a soft thresholding function and regularization. To solve this problem, we propose a novel unfolded network with residual connection to optimize threshold selection, which is an end-to-end deep data-driven adaptive learning scheme. Moreover, we designed a module called STConv (Structure and Texture reconstruction Convolution), which comprises two blocks: structure reconstruction block (SR) and texture reconstruction block (TR); the SR block uses a separate-and-reconstruct approach to suppress structure redundancy, while the TR block employs a split-transform-and-fuse strategy to eliminate texture redundancy. Experiments demonstrate that the proposed ARR-Net achieves superior performance compared to existing methods.