  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.
