Discrete tomography based on a modified SIRT algorithm

Filtered Back Projection and Simultaneous Iterative Reconstruction Technique (SIRT) are the most popular reconstruction algorithms in electron tomography. In both cases every TEM image is smeared back into object space along the original pathway (so-called back-projection). Both methods produce a blurring of the reconstructed objects, which affects the segmentation step after reconstruction. For high quality reconstructions with these standard reconstruction algorithms a large number of images are required, with typical tilt ranges of around +/-70° and tilt increments of 2°. As a result, issues of sample preparation and beam sensitivity have frequently become the limiting factor for obtaining high resolution data. If a sample consists of only a few different objects having different densities, a discrete reconstruction algorithm can be used, taking advantage of the reduced number of possible values in the reconstructed volume. As a consequence of the drastic reduction of the number of potential solutions, high quality tomographic reconstructions can be obtained with significantly smaller data sets, as demonstrated in electron tomography by the Discrete Algebraic Reconstruction Technique (DART) [1]. For DART, the quality of the 3D starting model and the greyscale segmentation is essential. These input parameters are usually obtained from a preceding reconstruction with a standard algorithm such as SIRT. Given that SIRT tends to distribute intensities to a bigger volume, these grey values are always underestimated and a large number of exposures is necessary to obtain good input parameters. For this reason, the initial SIRT reconstruction was modified by an additional " masking " step [2]. The mask is an approximation of the real object volume obtained from real measurement data. In each SIRT iteration step all voxels outside the mask will be set to zero. As a consequence, the intensity that a standard SIRT reconstruction would have scattered over " vacuum voxels " is now added to the object's voxels and increases their grey value. The reconstruction by masked SIRT is used as input for DART, which is then applied to the whole volume without the use of a mask. To reconstruct individual particles, a mask is calculated by subtracting the mean value from all projections, setting positive values to one and negative values to zero (Fig. 1). Afterwards, a volume is reconstructed with these " black and white " projections using one simple back-projection step. Every voxel encountering a zero value at least once during the back-projections is defined as vacuum. The remaining …