Sparse image reconstruction techniques have been used to recover high frequency information lost during the acquisition process in different imaging domains, such as ultrasound, synthetic aperture radar, optical microscopy, and astronomical and microscopic imaging. In this work, a signal processing framework is proposed to estimate the Point Spread Function (PSF) of the dark-field subsurface microscopy system from observation data. This PSF is incorporated into an image reconstruction framework, which can be formulated with two different image reconstruction techniques, regularized image reconstruction and dictionary-based image reconstruction. It is observed that both techniques provide at least 12% resolution improvement; lines with 224 nm spacing were localized after resolution improvement while lines with 252 nm spacing are at the limit of localization in experimental data. However, dictionary-based image reconstruction provides higher edge resolution and maintains the homogeneity of the intensity within the structures.