DeconvolutionLab2: An open-source software for deconvolution microscopy.

Images in fluorescence microscopy are inherently blurred due to the limit of diffraction of light. The purpose of deconvolution microscopy is to compensate numerically for this degradation. Deconvolution is widely used to restore fine details of 3D biological samples. Unfortunately, dealing with deconvolution tools is not straightforward. Among others, end users have to select the appropriate algorithm, calibration and parametrization, while potentially facing demanding computational tasks. To make deconvolution more accessible, we have developed a practical platform for deconvolution microscopy called DeconvolutionLab. Freely distributed, DeconvolutionLab hosts standard algorithms for 3D microscopy deconvolution and drives them through a user-oriented interface. In this paper, we take advantage of the release of DeconvolutionLab2 to provide a complete description of the software package and its built-in deconvolution algorithms. We examine several standard algorithms used in deconvolution microscopy, notably: Regularized inverse filter, Tikhonov regularization, Landweber, Tikhonov-Miller, Richardson-Lucy, and fast iterative shrinkage-thresholding. We evaluate these methods over large 3D microscopy images using simulated datasets and real experimental images. We distinguish the algorithms in terms of image quality, performance, usability and computational requirements. Our presentation is completed with a discussion of recent trends in deconvolution, inspired by the results of the Grand Challenge on deconvolution microscopy that was recently organized.

Design of Steerable Wavelets to Detect Multifold Junctions.

We propose a framework for the detection of junctions in images. Although the detection of edges and key points is a well examined and described area, the multiscale detection of junction centers, especially for odd orders, poses a challenge in pattern analysis. The goal of this paper is to build optimal junction detectors based on 2D steerable wavelets that are polar-separable in the Fourier domain. The approaches we develop are general and can be used for the detection of arbitrary symmetric and asymmetric junctions. The backbone of our construction is a multiscale pyramid with a radial wavelet function where the directional components are represented by circular harmonics and encoded in a shaping matrix. We are able to detect M -fold junctions in different scales and orientations. We provide experimental results on both simulated and real data to demonstrate the effectiveness of the algorithm.

Optimized Kaiser-Bessel Window Functions for Computed Tomography.

Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform independent of the direction. In this paper, we aim at optimizing the parameters of these basis functions. We present a formalism based on the theory of approximation and point out the importance of the partition-of-unity condition. While we prove that, for compact-support functions, this condition is incompatible with isotropy, we show that minimizing the deviation from the partition of unity condition is highly beneficial. The numerical results confirm that the proposed tuning of the Kaiser-Bessel window functions yields the best performance.

FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data.

Super resolution microscopy such as STORM and (F)PALM is now a well known method for biological studies at the nanometer scale. However, conventional imaging schemes based on sparse activation of photo-switchable fluorescent probes have inherently slow temporal resolution which is a serious limitation when investigating live-cell dynamics. Here, we present an algorithm for high-density super-resolution microscopy which combines a sparsity-promoting formulation with a Taylor series approximation of the PSF. Our algorithm is designed to provide unbiased localization on continuous space and high recall rates for high-density imaging, and to have orders-of-magnitude shorter run times compared to previous high-density algorithms. We validated our algorithm on both simulated and experimental data, and demonstrated live-cell imaging with temporal resolution of 2.5 seconds by recovering fast ER dynamics.

Fast iterative reconstruction of differential phase contrast X-ray tomograms.

Differential phase-contrast is a recent technique in the context of X-ray imaging. In order to reduce the specimen's exposure time, we propose a new iterative algorithm that can achieve the same quality as FBP-type methods, while using substantially fewer angular views. Our approach is based on 1) a novel spline-based discretization of the forward model and 2) an iterative reconstruction algorithm using the alternating direction method of multipliers. Our experimental results on real data suggest that the method allows to reduce the number of required views by at least a factor of four.

Constrained regularized reconstruction of X-ray-DPCI tomograms with weighted-norm.

In this paper we introduce a new reconstruction algorithm for X-ray differential phase-contrast Imaging (DPCI). Our approach is based on 1) a variational formulation with a weighted data term and 2) a variable-splitting scheme that allows for fast convergence while reducing reconstruction artifacts. In order to improve the quality of the reconstruction we take advantage of higher-order total-variation regularization. In addition, the prior information on the support and positivity of the refractive index is considered, which yields significant improvement. We test our method in two reconstruction experiments involving real data; our results demonstrate its potential for in-vivo and medical imaging.

FAST WAVELET-BASED SINGLE-PARTICLE RECONSTRUCTION IN CRYO-EM.

This paper presents a novel algorithm for the 3D tomographic inversion problem that arises in single-particle electron cryo-microscopy (Cryo-EM). It is based on two key components: 1) a variational formulation that promotes sparsity in the wavelet domain and 2) the Toeplitz structure of the combined projection/back-projection operator. The first idea has proven to be very effective for the recovery of piecewise-smooth signals, which is confirmed by our numerical experiments. The second idea allows for a computationally efficient implementation of the reconstruction procedure, using only one circulant convolution per iteration.

A fast multilevel algorithm for wavelet-regularized image restoration.

We present a multilevel extension of the popular "thresholded Landweber" algorithm for wavelet-regularized image restoration that yields an order of magnitude speed improvement over the standard fixed-scale implementation. The method is generic and targeted towards large-scale linear inverse problems, such as 3-D deconvolution microscopy. The algorithm is derived within the framework of bound optimization. The key idea is to successively update the coefficients in the various wavelet channels using fixed, subband-adapted iteration parameters (step sizes and threshold levels). The optimization problem is solved efficiently via a proper chaining of basic iteration modules. The higher level description of the algorithm is similar to that of a multigrid solver for PDEs, but there is one fundamental difference: the latter iterates though a sequence of multiresolution versions of the original problem, while, in our case, we cycle through the wavelet subspaces corresponding to the difference between successive approximations. This strategy is motivated by the special structure of the problem and the preconditioning properties of the wavelet representation. We establish that the solution of the restoration problem corresponds to a fixed point of our multilevel optimizer. We also provide experimental evidence that the improvement in convergence rate is essentially determined by the (unconstrained) linear part of the algorithm, irrespective of the type of wavelet. Finally, we illustrate the technique with some image deconvolution examples, including some real 3-D fluorescence microscopy data.