The paper presents a method for obtaining images in the study of the spatial structure of X-ray radiation of laser plasma with a new type of coded masks. In these experiments, a special type of self-supporting structure was chosen for the coded aperture. The shadow image created by the radiation passing through the aperture was recorded with a fluorescent imaging plate. An iterative algorithm based on a probabilistic approach to solving ill-posed problems was used to reconstruct the source image. The stability of the solution of the iterative method for masks of the considered type is studied, the results of applying the method for processing experimental data are presented, and the obtained images are compared with the images recorded with a pinhole camera. It has been established that the coded aperture used makes it possible to increase the sensitivity of the recording system by 2–3 orders of magnitude, while its use in combination with the developed mathematical algorithm allows one to obtain a higher spatial resolution than with a pinhole camera.