The input numerical aperture (NA) of multimode fiber (MMF) can be effectively increased by placing turbid media at the input end of the MMF. This provides the potential for high-resolution imaging through the MMF. While the input NA is increased, the number of propagation modes in the MMF and hence the output NA remains the same. This makes the image reconstruction process underdetermined and may limit the quality of the image reconstruction. In this paper, we aim to improve the signal to noise ratio (SNR) of the image reconstruction in imaging through MMF. We notice that turbid media placed in the input of the MMF transforms the incoming waves into a better format for information transmission and information extraction. We call this transformation as holistic random (HR) encoding of turbid media. By exploiting the HR encoding, we make a considerable improvement on the SNR of the image reconstruction. For efficient utilization of the HR encoding, we employ sparse representation (SR), a relatively new signal reconstruction framework when it is provided with a HR encoded signal. This study shows for the first time to our knowledge the benefit of utilizing the HR encoding of turbid media for recovery in the optically underdetermined systems where the output NA of it is smaller than the input NA for imaging through MMF.
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