We present a multiresolution reconstruction framework for single-particle analysis (SPA). The representation of 3D objects with scaled basis functions permits the reconstruction of volumes at any desired scale in the real-space. With this tool, one can now select a level of “coarseness” for the reconstruction that is well adapted to the current under-determination of the measurements during the refinement procedure (e.g., few projection angles). In particular, we show that reconstruction performed at coarse scale is more robust to error on angles and permits gains in computational speed. A key component of the proposed multiresolution scheme is its fast implementation. The costly step of the reconstruction — which was previously hindering the use of advanced iterative methods in SPA — is formulated as a discrete convolution with cost independent upon the number of projection directions. The inclusion of the CTF inside the imaging matrix is also done at no extra computational cost. Finally, by permitting full 3D regularisation, the framework is by itself a robust alternative to direct methods for performing reconstruction in adverse imaging conditions.
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