The utilization of hyperspectral imaging in remote sensing has seen an increasing trend, as it enables to capture a greater amount of information. In this context, emerging snapshot sensors based on compressed sensing have been employed for various remote sensing applications. This work presents a prospective study by proposing a method to evaluate the performances we can expect when reconstructing data from a compressed sensing imager, the Double-Disperser Coded Aperture Snapshot Spectral Imager on an embedded system, i.e. on either a Graphics Processing Unit or a Field-Programmable Gate Arrays. This is original in the literature since most compressive sensing works focus on reconstruction quality and overlook the requirements for real-time, namely computational cost and data bandwidth. Moreover, works that use an embedded system are even more scarse. The study introduces methods to enhance these restrictions and assesses the resulting improvements. The study's findings support the use of Disperser Coded Aperture Snapshot Spectral Imager for remote sensing applications, potentially enabling a smaller sensor size.