Imaging with X-rays is a challenging field, due to the optical properties of X-rays. The fabrication of appropriate optics is usually expensive and requires an elaborate manufacturing process. One simpler and less expensive possibility of imaging high energy radiation is coded aperture imaging, a technique well established in astrophysics and also used in nuclear medicine or radiation detection, e.g., for nuclear decommissioning. Our aim is to adapt coded aperture imaging for X-ray fluorescence spectroscopy in the nearfield. In this work we show theoretical considerations and preliminary simulations of image formation through a coded aperture and three different reconstruction methods to prepare the experiments. We used a new mask based on an inverted modified uniformly redundant array (MURA) that could be used for the construction of a decoding mask for all investigated geometrical arrangements. The most commonly used reconstruction method, convoluting the detected image with a decoding mask, does not always deliver satisfactory results. This is more noticeable for small distances between the object, mask and detector. Hence, we developed two new reconstruction methods, one based on iterative algebraic optimization and another one based on a genetic algorithm. Both show good performance even in those cases where the convolution method fails. This provides a basis for further investigations of the ideal parameters for near field coded aperture imaging and refinements of the algorithms. We performed first measurements with a coded aperture at the BAMline at BESSY II and could successfully reconstruct a test object from the obtained recorded images.