Standard image sensors feature dynamic range about 60 to 70 dB while the light flux of natural scenes may be over 120 dB. Most imagers dedicated to address such dynamic ranges, need specific, and large pixels. However, canonical imagers can be used for high dynamic range (HDR) by performing multicapture acquisitions to compensate saturation. This technique is made possible at the expense of the need for large memory requirements and an increase of the overall acquisition time. On the other hand, the implementation of compressive sensing (CS) raises the same issues regarding the modifications of both the pixel and the read-out circuitry. Assuming HDR images are sufficiently sparse, CS claims they can be reconstructed from few random linear measurements. A novel CS-based image sensor design is presented in this paper allowing a compressive acquisition without changing the classical pixel design, as well as the overall sensor architecture. In addition to regular CS, HDR CS is enabled thanks to specific time diagrams of the control signals. An alternative nondestructive column-based readout mode constitutes the main change compared to a traditional functioning. The HDR reconstruction, which is also presented in this paper, is based on merging the information of multicapture compressed measurements while taking into account noise sources and nonlinearities introduced by both the proposed acquisition scheme and its practical implementation.