Javier Vargas

Two-step demodulation based on the Gram-Schmidt orthonormalization method

This Letter presents an efficient, fast, and straightforward two-step demodulating method based on a Gram-Schmidt (GS) orthonormalization approach. The phase-shift value has not to be known and can take any value inside the range (0,2π), excluding the singular case, where it corresponds to π. The proposed method is based on determining an orthonormalized interferogram basis from the two supplied interferograms using the GS method. We have applied the proposed method to simulated and experimental interferograms, obtaining satisfactory results. A complete MATLAB software package is provided at http://goo.gl/IZKF3.

Two-step interferometry by a regularized optical flow algorithm

A two-step phase-shifting method, that can demodulate open- and closed-fringed patterns without local sign ambiguity is presented. The proposed method only requires a constant phase-shift between the two interferograms. This phase-shift does not need to be known and can take any value inside the range (0, 2π), excluding the singular case where it corresponds to π. The proposed method is based on determining first the fringe direction map by a regularized optical flow algorithm. After that, we apply the spiral phase transform (SPT) to one of the fringe patterns and we determine its quadrature signal using the previously determined direction. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results. A complete MATLAB software package is provided in [http://goo.gl/Snnz7].

Fast two-dimensional simultaneous phase unwrapping and low-pass filtering.

Here, we present a fast algorithm for two-dimensional (2D) phase unwrapping which behaves as a recursive linear filter. This linear behavior allows us to easily find its frequency response and stability conditions. Previously, we published a robust to noise recursive 2D phase unwrapping system with smoothing capabilities. But our previous approach was rather heuristic in the sense that not general 2D theory was given. Here an improved and better understood version of our previous 2D recursive phase unwrapper is presented. In addition, a full characterization of it is shown in terms of its frequency response and stability. The objective here is to extend our previous unwrapping algorithm and give a more solid theoretical foundation to it.

Spatial carrier phase-shifting algorithm based on principal component analysis method

A non-iterative spatial phase-shifting algorithm based on principal component analysis (PCA) is proposed to directly extract the phase from only a single spatial carrier interferogram. Firstly, we compose a set of phase-shifted fringe patterns from the original spatial carrier interferogram shifting by one pixel their starting position. Secondly, two uncorrelated quadrature signals that correspond to the first and second principal components are extracted from the phase-shifted interferograms by the PCA algorithm. Then, the modulating phase is calculated from the arctangent function of the two quadrature signals. Meanwhile, the main factors that may influence the performance of the proposed method are analyzed and discussed, such as the level of random noise, the carrier-frequency values and the angle of carrier-frequency of fringe pattern. Numerical simulations and experiments are given to demonstrate the performance of the proposed method and the results show that the proposed method is fast, effectively and accurate. The proposed method can be used to on-line detection fields of dynamic or moving objects.

Alignment of direct detection device micrographs using a robust Optical Flow approach

The introduction of direct detection devices in cryo-EM has shown that specimens present beam-induced motion (BIM). Consequently, in this work, we develop a BIM correction method at the image level, resulting in an integrated image in which the in-plane BIM blurring is compensated prior to particle picking. The methodology is based on a robust Optical Flow (OF) approach that can efficiently correct for local movements in a rapid manner. The OF works particularly well if the BIM pattern presents a substantial degree of local movements, which occurs in our data sets for Falcon II data. However, for those cases in which the BIM pattern corresponds to global movements, we have found it advantageous to first run a global motion correction approach and to subsequently apply OF. Additionally, spatial analysis of the Optical Flow allows for quantitative analysis of the BIM pattern. The software that incorporates the new approach is available in XMIPP (http://xmipp.cnb.csic.es).

Asymmetric cryo-EM reconstruction of phage MS2 reveals genome structure in situ

In single-stranded ribonucleic acid (RNA) viruses, virus capsid assembly and genome packaging are intertwined processes. Using cryo-electron microscopy and single particle analysis we determined the asymmetric virion structure of bacteriophage MS2, which includes 178 copies of the coat protein, a single copy of the A-protein and the RNA genome. This reveals that in situ, the viral RNA genome can adopt a defined conformation. The RNA forms a branched network of stem-loops that almost all allocate near the capsid inner surface, while predominantly binding to coat protein dimers that are located in one-half of the capsid. This suggests that genomic RNA is highly involved in genome packaging and virion assembly.

Efficient initial volume determination from electron microscopy images of single particles.

MOTIVATION Structural information of macromolecular complexes provides key insights into the way they carry out their biological functions. The reconstruction process leading to the final 3D map requires an approximate initial model. Generation of an initial model is still an open and challenging problem in single-particle analysis. RESULTS We present a fast and efficient approach to obtain a reliable, low-resolution estimation of the 3D structure of a macromolecule, without any a priori knowledge, addressing the well-known issue of initial volume estimation in the field of single-particle analysis. The input of the algorithm is a set of class average images obtained from individual projections of a biological object at random and unknown orientations by transmission electron microscopy micrographs. The proposed method is based on an initial non-lineal dimensionality reduction approach, which allows to automatically selecting representative small sets of class average images capturing the most of the structural information of the particle under study. These reduced sets are then used to generate volumes from random orientation assignments. The best volume is determined from these guesses using a random sample consensus (RANSAC) approach. We have tested our proposed algorithm, which we will term 3D-RANSAC, with simulated and experimental data, obtaining satisfactory results under the low signal-to-noise conditions typical of cryo-electron microscopy. AVAILABILITY The algorithm is freely available as part of the Xmipp 3.1 package [http://xmipp.cnb.csic.es]. CONTACT jvargas@cnb.csic.es SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

FASTDEF: Fast defocus and astigmatism estimation for high-throughput transmission electron microscopy

In this work we present a fast and automated algorithm for estimating the contrast transfer function (CTF) of a transmission electron microscope. The approach is very suitable for High Throughput work because: (a) it does not require any initial defocus estimation, (b) it is almost an order of magnitude faster than existing approaches, (c) it opens the way to well-defined extensions to the estimation of higher order aberrations, at the same time that provides defocus and astigmatism estimations comparable in accuracy to well established methods, such as Xmipp and CTFFIND3 approaches. The new algorithm is based on obtaining the wrapped modulating phase of the power spectra density pattern by the use of a quadrature filter. This phase is further unwrapped in order to obtain the continuous and smooth absolute phase map; then a Zernike polynomial fitting is performed and the defocus and astigmatism parameters are determined. While the method does not require an initial estimation of the defocus parameters or any non-linear optimization procedure, these approaches can be used if further refinement is desired. Results of the CTF estimation method are presented for standard negative stained images, cryo-electron microscopy images in the absence of carbon support, as well as micrographs with only ice. Additionally, we have also tested the proposed method with micrographs acquired from tilted and untilted samples, obtaining good results. The algorithm is freely available as a part of the Xmipp package [http://xmipp.cnb.csic.es].

Windowed phase unwrapping using a first-order dynamic system following iso-phase contours.

In this work, we show a windowed phase-unwrapping technique that uses a first-order dynamic system and scans the phase following its iso-phase contours. In previous works, we have shown that low-pass first-order dynamic systems are very robust and useful in phase-unwrapping problems. However, it is well known that all phase-unwrapping methods have a minimum signal-to-noise ratio that they tolerate. This paper shows that scanning the phase within local windows and using a path following strategy, the first-order unwrapping method increases its tolerance to noise. In this way, using the improved approach, we can unwrap phase maps where the basic dynamic phase-unwrapping system fails. Tests and results are given, as well as the source code in order to show the performance of the proposed method.

Particle quality assessment and sorting for automatic and semiautomatic particle-picking techniques

Three-dimensional reconstruction of biological specimens using electron microscopy by single particle methodologies requires the identification and extraction of the imaged particles from the acquired micrographs. Automatic and semiautomatic particle selection approaches can localize these particles, minimizing the user interaction, but at the cost of selecting a non-negligible number of incorrect particles, which can corrupt the final three-dimensional reconstruction. In this work, we present a novel particle quality assessment and sorting method that can separate most erroneously picked particles from correct ones. The proposed method is based on multivariate statistical analysis of a particle set that has been picked previously using any automatic or manual approach. The new method uses different sets of particle descriptors, which are morphology-based, histogram-based and signal to noise analysis based. We have tested our proposed algorithm with experimental data obtaining very satisfactory results. The algorithm is freely available as a part of the Xmipp 3.0 package [http://xmipp.cnb.csic.es].