Direct-conversion transceivers are the predominating architecture in current mobile communication systems. Despite many advantages, this topology suffers from unavoidable mismatches in the analog part, which causes imbalance between the in-phase and quadrature (I/Q) component. In this paper, we present a novel fully digital, blind I/Q imbalance compensation algorithm that features extremely low computational complexity and high compensation performance for a wide range of input signal types. Different to many state-of-the-art compensation schemes, the approach is not based on a gradient descent optimization and does not require any global feedback. This simplifies the implementation at high data rates and reduces the configuration effort to a minimum. For comparison, we examine an existing method of moment-based estimator with similar properties, for which we also provide the detailed insights beyond available literature. For both algorithms, we provide a rigorous mathematical analysis, which is supported by simulations with a focus on various long-term evolution (LTE) signal types. In addition, hardware architectures, including field-programmable gate array (FPGA) verification, are presented for both algorithms.