Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy

Department of NanoBiophotonics, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, Goettingen, Germany.
Journal of Microscopy (Impact Factor: 2.15). 05/2009; 234(1):47-61. DOI: 10.1111/j.1365-2818.2009.03150.x
Source: PubMed

ABSTRACT The methods of image deconvolution are important for improving the quality of the detected images in the different modalities of fluorescence microscopy such as wide-field, confocal, two-photon excitation and 4Pi. Because deconvolution is an ill-posed problem, it is, in general, reformulated in a statistical framework such as maximum likelihood or Bayes and reduced to the minimization of a suitable functional, more precisely, to a constrained minimization, because non-negativity of the solution is an important requirement. Next, iterative methods are designed for approximating such a solution. In this paper, we consider the Bayesian approach based on the assumption that the noise is dominated by photon counting, so the likelihood is of the Poisson-type, and that the prior is edge-preserving, as derived from a simple Markov random field model. By considering the negative logarithm of the a posteriori probability distribution, the computation of the maximum a posteriori (MAP) estimate is reduced to the constrained minimization of a functional that is the sum of the Csiszár I-divergence and a regularization term. For the solution of this problem, we propose an iterative algorithm derived from a general approach known as split-gradient method (SGM) and based on a suitable decomposition of the gradient of the functional into a negative and positive part. The result is a simple modification of the standard Richardson-Lucy algorithm, very easily implementable and assuring automatically the non-negativity of the iterates. Next, we apply this method to the particular case of confocal microscopy for investigating the effect of several edge-preserving priors proposed in the literature using both synthetic and real confocal images. The quality of the restoration is estimated both by computation of the Kullback-Leibler divergence of the restored image from the detected one and by visual inspection. It is observed that the noise artefacts are considerably reduced and desired characteristics (edges and minute features as islets) are retained in the restored images. The algorithm is stable, robust and tolerant at various noise (Poisson) levels. Finally, by remarking that the proposed method is essentially a scaled gradient method, a possible modification of the algorithm is briefly discussed in view of obtaining fast convergence and reduction in computational time.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In a stimulated emission depletion (STED) microscope the region from which a fluorophore can spontaneously emit shrinks with the continued STED beam action after the excitation event. This fact has been recently used to implement a versatile, simple and cheap STED microscope that uses a pulsed excitation beam, a STED beam running in continuous-wave (CW) and a time-gated detection: By collecting only the delayed (with respect to the excitation events) fluorescence, the STED beam intensity needed for obtaining a certain spatial resolution strongly reduces, which is fundamental to increase live cell imaging compatibility. This new STED microscopy implementation, namely gated CW-STED, is in essence limited (only) by the reduction of the signal associated with the time-gated detection. Here we show the recent advances in gated CW-STED microscopy and related methods. We show that the time-gated detection can be substituted by more efficient computational methods when the arrival-times of all fluorescence photons are provided. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
    Photonics West - Lasers and Applications in Science and Engineering, San Francisco, California, United States; 02/2015
  • [Show abstract] [Hide abstract]
    ABSTRACT: Confocal microscopy has become an essential tool to explore biospecimens in 3D. Confocal microcopy images are still degraded by out-of-focus blur and Poisson noise. Many deconvolution methods including the Richardson-Lucy (RL) method, Tikhonov method and split-gradient (SG) method have been well received. The RL deconvolution method results in enhanced image quality, especially for Poisson noise. Tikhonov deconvolution method improves the RL method by imposing a prior model of spatial regularization, which encourages adjacent voxels to appear similar. The SG method also contains spatial regularization and is capable of incorporating many edge-preserving priors resulting in improved image quality. The strength of spatial regularization is fixed regardless of spatial location for the Tikhonov and SG method. The Tikhonov and the SG deconvolution methods are improved upon in this study by allowing the strength of spatial regularization to differ for different spatial locations in a given image. The novel method shows improved image quality. The method was tested on phantom data for which ground truth and the point spread function are known. A Kullback-Leibler (KL) divergence value of 0.097 is obtained with applying spatially variable regularization to the SG method, whereas KL value of 0.409 is obtained with the Tikhonov method. In tests on a real data, for which the ground truth is unknown, the reconstructed data show improved noise characteristics while maintaining the important image features such as edges.
    Journal of Microscopy 06/2014; 255(2). DOI:10.1111/jmi.12141 · 2.15 Impact Factor
  • Source

Full-text (4 Sources)

Available from
Jun 6, 2014