Self-imaging beams consisting of three-dimensional intensity voids are generated via photorefractive volume holography. Reconstruction of a volume hologram recorded at 594 nm is performed with a Bessel readout beam. The holographic output is similar in appearance to a Bessel beam, with the central spot oscillating between maximum and zero intensity over a propagation distance of 10 to 55 cm. The oscillation period for the on-axis intensity is 30 cm. The reconstruction is capable of self-healing, with a fully recovered central core after the beam propagates 40 cm. Dual-wavelength reconstruction at 632.8 nm produces an output beam with similar self-imaging and self-healing properties. A theoretical framework based on the interference of a plane wave and a Bessel beam simultaneously reconstructed from a volume hologram is able to describe our experimental results.