Minimal mutual coherence of discrete noiselets and Haar wavelets makes this pair of bases an essential choice for the measurement and compression matrices in compressed-sensing-based single-pixel detectors. In this paper, we propose an efficient way of using complex-valued and nonbinary noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators and incoherent illumination. The proposed method allows us to determine m complex noiselet coefficients from m+1 binary sampling measurements. Further, we introduce a modification to the complex fast noiselet transform, which enables computationally efficient real-time generation of the binary noiselet-based patterns using efficient integer calculations on bundled patterns. The proposed method is verified experimentally with a single-pixel camera system using a binary spatial light modulator.