Projection images, such as those routinely acquired in radiological practice, are difficult to analyze because multiple 3D structures superimpose at a single point in the 2D image. Removal of particular superimposed structures may improve interpretation of these images, both by humans and by computers. This work therefore presents a general method to isolate and suppress structures in 2D projection images. The focus is on elongated structures, which allows an intensity model of a structure of interest to be extracted using local information only. The model is created from profiles sampled perpendicular to the structure. Profiles containing other structures are detected and removed to reduce the influence on the model. Subspace filtering, using blind source separation techniques, is applied to separate the structure to be suppressed from other structures. By subtracting the modeled structure from the original image a structure suppressed image is created. The method is evaluated in four experiments. In the first experiment ribs are suppressed in 20 artificial radiographs simulated from 3D lung computed tomography (CT) images. The proposed method with blind source separation and outlier detection shows superior suppression of ribs in simulated radiographs, compared to a simplified approach without these techniques. Additionally, the ability of three observers to discriminate between patches containing ribs and containing no ribs, as measured by the Area under the Receiver Operating Characteristic curve (AUC), reduced from 0.99-1.00 on original images to 0.75-0.84 on suppressed images. In the second experiment clavicles are suppressed in 253 chest radiographs. The effect of suppression on clavicle visibility is evaluated using the clavicle contrast and border response, showing a reduction of 78\% and 34\% respectively. In the third experiment nodules extracted from CT were simulated close to the clavicles in 100 chest radiographs. It was found that after suppression contrast of the nodules was higher than of the clavicles and 2.46 respectively). In the fourth experiment catheters were suppressed in chest radiographs. The ability of three observers to discriminate between patches originating from 36 images with and 21 images without catheters, as measured by the AUC, reduced from 0.98-0.99 on original images to 0.64-0.74 on suppressed images. We conclude that the presented method can markedly reduce the visibility of elongated structures in chest radiographs and shows potential to enhance diagnosis.