Methods and systems are described for digitally reconstructing an unknown 3D structure of a target molecule using orthogonal extension. A plurality of 2D images of the target molecule are captured by an imaging system. An estimated low-order moment of the unknown 3D structure (e.g., a covariance matrix) is calculated based on the 2D images. A homologous molecule having a known 3D structure is identified and at least one expansion coefficient of the known structure of the homologous molecule is determined. At least one estimated expansion coefficient for the unknown structure is calculated based at least in part on the estimated low order moment of the unknown structure and the at least one expansion coefficient of the known structure. An estimated 3D reconstruction of the target molecule is then generated based on the at least one estimated expansion coefficient for the unknown structure of the target molecule.