Measurement matrix construction by specklegrams from step index multimode fiber and its application in compressive sensing

Compressive sensing (CS) is a recently developed theory which allows reconstruction of sparse signals with the number of measurements much lower than that required by the Nyquist sampling, and sensing the signals with a measurement matrix (MM) is one of the indispensable key procedures. Based on the specklegrams of multimode fiber (MMF) with offset-launching and coreless multimode fiber (CMF) with center-launching, MM was constructed and applied in CS. The constructed MMs provide improved performances compared with the conventional Gaussian MM in CS when applied to image reconstruction. Specklegrams of MMF with different launching offsets and CMF with different wavelengths were respectively used to construct the MMs by different construction methods, which demonstrated the flexibility of the combination of fiber specklegrams to get a MM. By careful comparisons, it can be concluded that MMs based on the fiber specklegrams perform better in providing a good Peak Signal to Noise Ratio. Moreover, the construction methods can be easily implemented, which is highly promising for compressive sensing.