A 4D computational incoherent imaging technique using accelerating Airy beams (A2-beams) and nonlinear reconstruction (NLR) has been developed. The phase mask was designed as a binary version for the generation of a sparse random array of A2-beams. The imaging process consist of three steps. In the first step a 4D point spread function (PSF) was recorded at different wavelengths and depths. In the next step, a multicolor, multiplane object was loaded and a single camera shot was recorded. Finally, the 4D information of the object was reconstructed by processing the object intensity distribution and 4D PSFs. The simulation results for the imaging concept are presented.