  Radio imaging is rapidly gaining prominence in the design of future
communication systems, with the potential to utilize reconfigurable intelligent
surfaces (RISs) as imaging apertures. Although the sparsity of targets in
three-dimensional (3D) space has led most research to adopt compressed sensing
(CS)-based imaging algorithms, these often require substantial computational
and memory burdens. Drawing inspiration from conventional Fourier transform
(FT)-based imaging methods, our research seeks to accelerate radio imaging in
RIS-aided communication systems. To begin, we introduce a two-stage wavenumber
domain 3D imaging technique: first, we modify RIS phase shifts to recover the
equivalent channel response from the user equipment to the RIS array,
subsequently employing traditional FT-based wavenumber domain methods to
produce target images. We also determine the diffraction resolution limits of
the system through k-space analysis, taking into account factors including
system bandwidth, transmission direction, operating frequency, and the angle
subtended by the RIS. Addressing the challenge of limited pilots in
communication systems, we unveil an innovative algorithm that merges the
strengths of both FT- and CS-based techniques by substituting the expansive
sensing matrix with FT-based operators. Our simulation outcomes confirm that
our proposed FT-based methods achieve high-quality images while demanding few
time, memory, and communication resources.
