We provide an approach to improve the quality of image reconstruction in wide-field imaging through turbid media (WITM). In WITM, a calibration stage which measures the transmission matrix (TM), the set of responses of turbid medium to a set of plane waves with different incident angles, is preceded to the image recovery. Then, the TM is used for estimation of object image in image recovery stage. In this work, we aim to estimate highly resolved angular spectrum and use it for high quality image reconstruction. To this end, we propose to perform a dense sampling for TM measurement in calibration stage with finer incident angle spacing. In conventional approaches, incident angle spacing is made to be large enough so that the columns in TM are out of memory effect of turbid media. Otherwise, the columns in TM are correlated and the inversion becomes difficult. We employ compressed sensing (CS) for a successful high resolution angular spectrum recovery with dense sampled TM. CS is a relatively new information acquisition and reconstruction framework and has shown to provide superb performance in ill-conditioned inverse problems. We observe that the image quality metrics such as contrast-to-noise ratio and mean squared error are improved and the perceptual image quality is improved with reduced speckle noise in the reconstructed image. This results shows that the WITM performance can be improved only by executing dense sampling in the calibration stage and with an efficient signal reconstruction framework without elaborating the overall optical imaging systems.