Current high-contrast imaging systems implement wavefront control using traditional deformable mirrors developed for atmospheric turbulence correction, which require large strokes, high-speed, and continuous phase correction. However, high-contrast imaging has different requirements. Thus, developing a specialized deformable mirror for this application able to meet the demanding requirements of future exoplanet imaging flagship missions is valuable for the exoplanet scientific community. In this paper, we propose a novel wavefront control approach, called Sparse Wave-Front Control (SWFC), which enables high-contrast imaging using sparse phase changes on the active surface re-directing coherent starlight to null speckles. To validate SWFC, we simulated a telescope equipped with a Phase Induced Amplitude Apodization (PIAA) coronagraph and a 100 by 100 actuator sparse Deformable Mirror to null speckles caused by the optical system aberrations. We modeled the mirror as a flat surface where narrow gaussian influence functions represent actuators. We performed wavefront control utilizing Electric Field Conjugation achieving 6.7e-11 mean contrast between 3 to 35λ/D in monochromatic light and 7.4e-11 in 10% broadband light. In the second part of this paper, we propose an approach to manufacture Sparse Deformable Mirrors utilizing photosensitive polymers, which could be placed below the mirror coating and can be photonically actuated by back illumination through the mirror substrate.