Microstructure reconstruction and characterization (MCR) is one of the key tenets enabling the digitization and acceleration of materials engineering. MCR is specifically required for the following tasks: (i) generating a 3D computational domain from 2D data, e.g., microscopy image; (ii) reconstructing a small, periodic domain from a large, aperiodic CT scan; (iii) generating a set of statistical volume elements from a single reference; and (iv) improving microstructure datasets through sampling and interpolation in the descriptor space, followed by microstructure reconstruction. This work focuses specifically on descriptor-based MCR, where the statistical microstructure description is provided explicitly. Compared to machine learning-based MCR, descriptor-based MCR has the advantage of not requiring a data set. Rather, it can be utilized to generate it, enabling data-driven modeling and simulation on otherwise inadequate data sets. A significant speedup with respect to the Yeong-Torquato algorithm was recently achieved by restricting the microstructure morphology quantification to differentiable descriptors [1, 2]. This enables the use of gradient-based optimizers, which converge significantly faster than gradient-free, stochastic methods. This is known as differentiable MCR and implemented in MCRpy [3]. This contribution presents a leap forward in terms of computational and memory efficiency. Rather than merely passing the gradients of the descriptor mismatch to a quasi-Newton optimization algorithm, custom (approximate) gradient projection operators can be defined. A well-known algorithm from the texture synthesis literature, the Portilla-Simoncelli algorithm [4], is identified as a method that follows this approach. However, it is restricted to 2D. After validating its applicability to microstructure data, a 2D-to-3D dimensionality extension is presented. [1] Seibert et al., Reconstructing random heterogeneous media through differentiable optimization, COMMAT, 2021 [2] Seibert et al., Descriptor-based reconstruction of three-dimensional microstructures through gradient-based optimization, Acta Materialia, 2022 [3] Seibert et al., Microstructure Characterization and Reconstruction in Python: MCRpy, IMMJ, 2022 [4] Portilla and Simoncelli, A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients, 2000