Structured illumination microscopy (SIM) has attracted considerable interest in superresolution, live-cell imaging because of its low light dose and high imaging speed. Obtaining a high-quality reconstruction image in SIM depends on the precise determination of the parameters of the fringe illumination pattern. The image recombination transform (IRT) algorithm is superior to other algorithms in obtaining the precise initial phase without any approximation, which is promising to provide a considerable solution to address the difficulty of initial phase estimation at low-modulation-depth conditions. However, the IRT algorithm only considers a phase shift of π/2, which limits its applications in general scenarios. In this letter, we present a general form of IRT algorithm suitable for arbitrary phase shifts, providing a powerful tool for parameter estimation in low signal-to-noise cases. To demonstrate the effectiveness of the enhanced IRT algorithm, we constructed a multicolor, structured illumination microscope and studied at super-resolution, the cargo traffic in HRPE cells, and monitored the movement of mitochondrial structures and microtubules in COS-7 cells. The custom SIM system using the enhanced IRT algorithm allows multicolor capability and a low excitation intensity fluorescence imaging less than 1 W/cm2. High-quality super-resolution images are obtained, which demonstrates the utility of this approach in imaging in the life sciences. © 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement