| Image reconstruction covers a wide range of physical applications from electron microscopy of molecular structures to radio astronomy of cosmic structures. In this work we will focus on molecular structures, namely biological macromolecules imaged by a transmission electron microscope (TEM) and then reconstructed from such images.; Biological macromolecules are classified into four broad subclasses: proteins, nucleic acids, polysaccharides and lipids. All of these macromolecules exhibit a complex structure which determines the interaction of the macromolecule with itself or with others. Particularly, proteins have a functional role which is not present in the other three types of macro-molecules. It is believed that this role is largely due to the three-dimensional structure they possess.; TEM technology has been commonly used to obtain reconstructions of macromolecular structures because of the meaningful information this technology produces. Algebraic Reconstruction Techniques (ART) are methods for the reconstruction of macromolecular complexes in TEM. After reconstruction, the approximation of the macromolecule is an imprecise approximation and is generally corrupted by noise.; Reconstructions with ART produce volumes expressed as linear combinations of some basis functions. Recently, spherically symmetric functions ( blobs) have been introduced as efficacious basis functions for reconstruction. We propose a method of selecting blob parameters to obtain accurate reconstructions and visual representations of the structure of macromolecular complexes.; ART produces the set of weights for the basis functions, i.e., the set of coefficients. In order to produce fast and accurate visual representations of macromolecules we propose a method that takes advantage of the properties of ART and blobs, together with simple thresholding of the set of coefficients, that identifies those blobs that may contribute to the formation of the macromolecule and, thus, simplifies the search for significant blobs.; One characteristic of biological macromolecules, which distinguishes them from specimens used in other fields, is that they frequently present some kind of symmetry. In fact, the functional form of many biological macromolecules is obtained by merging or joining several copies of one or several subunits. We propose to take advantage of the repetitive presence of subunits to improve the signal-to-noise ratio of the reconstruction of a macro-molecule. |
