Laser beams that can self-reconstruct their initial beam profile even in the presence of massive phase perturbations are able to propagate deeper into inhomogeneous media. This ability has crucial advantages for light sheet-based microscopy in thick media, such as cell clusters, embryos, skin or brain tissue or plants, as well as scattering synthetic materials. A ring system around the central intensity maximum of a Bessel beam enables its self-reconstruction, but at the same time illuminates out-of-focus regions and deteriorates image contrast. Here we present a detection method that minimizes the negative effect of the ring system. The beam's propagation stability along one straight line enables the use of a confocal line principle, resulting in a significant increase in image contrast. The axial resolution could be improved by nearly 100% relative to the standard light-sheet techniques using scanned Gaussian beams, while demonstrating self-reconstruction also for high propagation depths.