Analyzing the photoluminescence (PL) maps of semiconductors complementarily in time and wavelength allows to derive their key optoelectronic and transport properties. Up to now, separate acquisitions along time or wavelength had to be acquired for time and wavelength so that a comprehensive study of the dynamics was out of reach. We developed a 4D imaging setup that allows the simultaneous acquisition of spectral and temporal luminescence intensity with micrometric spatial resolution under the exact same experimental conditions. This novel setup relies on single pixel imaging, an approach that enables the reconstruction of the spatial information recorded from a higher resolution nonimaging detector. The sample PL signal is spatially modulated with different patterns by a digital micro-mirror device 1. We make use of this technique for the first time with a streak camera as a detector, allowing to record the PL intensity decays and spectrum for each pixel with very high temporal (<100ps) and spectral resolutions (< 1nm). A patent application has been filled. We demonstrate the use of this setup by characterizing III-V samples. We observe the spatial variations of a red shift occurring during the short time of the decay.