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Photoacoustic microscopy uses multiple wavelengths to measure concentrations of different absorbers. The speed of sound limits the shortest wavelength switching time to sub-microseconds, which is a bottleneck for high-speed broad-spectrum imaging. Via computational separation of overlapped signals, we can break the sound-speed limit on the wavelength switching time. This paper presents a new signal unmixing algorithm named two-step proximal gradient descent. It is advantageous in separating multiple wavelengths with long overlapping and high noise. In the simulation, we can unmix up to nine overlapped signals and successfully separate three overlapped signals with 12-ns delay and 15.9-dB signal-to-noise ratio. We apply this technique to separate three-wavelength photoacoustic images in microvessels. In vivo results show that the algorithm can successfully unmix overlapped multi-wavelength …