447 research outputs found
Blind Source Separation with Compressively Sensed Linear Mixtures
This work studies the problem of simultaneously separating and reconstructing
signals from compressively sensed linear mixtures. We assume that all source
signals share a common sparse representation basis. The approach combines
classical Compressive Sensing (CS) theory with a linear mixing model. It allows
the mixtures to be sampled independently of each other. If samples are acquired
in the time domain, this means that the sensors need not be synchronized. Since
Blind Source Separation (BSS) from a linear mixture is only possible up to
permutation and scaling, factoring out these ambiguities leads to a
minimization problem on the so-called oblique manifold. We develop a geometric
conjugate subgradient method that scales to large systems for solving the
problem. Numerical results demonstrate the promising performance of the
proposed algorithm compared to several state of the art methods.Comment: 9 pages, 2 figure
3D ab initio modeling in cryo-EM by autocorrelation analysis
Single-Particle Reconstruction (SPR) in Cryo-Electron Microscopy (cryo-EM) is
the task of estimating the 3D structure of a molecule from a set of noisy 2D
projections, taken from unknown viewing directions. Many algorithms for SPR
start from an initial reference molecule, and alternate between refining the
estimated viewing angles given the molecule, and refining the molecule given
the viewing angles. This scheme is called iterative refinement. Reliance on an
initial, user-chosen reference introduces model bias, and poor initialization
can lead to slow convergence. Furthermore, since no ground truth is available
for an unsolved molecule, it is difficult to validate the obtained results.
This creates the need for high quality ab initio models that can be quickly
obtained from experimental data with minimal priors, and which can also be used
for validation. We propose a procedure to obtain such an ab initio model
directly from raw data using Kam's autocorrelation method. Kam's method has
been known since 1980, but it leads to an underdetermined system, with missing
orthogonal matrices. Until now, this system has been solved only for special
cases, such as highly symmetric molecules or molecules for which a homologous
structure was already available. In this paper, we show that knowledge of just
two clean projections is sufficient to guarantee a unique solution to the
system. This system is solved by an optimization-based heuristic. For the first
time, we are then able to obtain a low-resolution ab initio model of an
asymmetric molecule directly from raw data, without 2D class averaging and
without tilting. Numerical results are presented on both synthetic and
experimental data
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