A Parallel Product-Convolution approach for representing the depth varying Point Spread Functions in 3D widefield microscopy based on principal component analysis

Keck Advanced Microscopy Center and the Dept. of Biochem. and Biophys., University of California at San Francisco, San Francisco, CA-94158, USA.
Optics Express (Impact Factor: 3.49). 03/2010; 18(7):6461-76. DOI: 10.1364/OE.18.006461
Source: PubMed


We address the problem of computational representation of image formation in 3D widefield fluorescence microscopy with depth varying spherical aberrations. We first represent 3D depth-dependent point spread functions (PSFs) as a weighted sum of basis functions that are obtained by principal component analysis (PCA) of experimental data. This representation is then used to derive an approximating structure that compactly expresses the depth variant response as a sum of few depth invariant convolutions pre-multiplied by a set of 1D depth functions, where the convolving functions are the PCA-derived basis functions. The model offers an efficient and convenient trade-off between complexity and accuracy. For a given number of approximating PSFs, the proposed method results in a much better accuracy than the strata based approximation scheme that is currently used in the literature. In addition to yielding better accuracy, the proposed methods automatically eliminate the noise in the measured PSFs.


Available from: Muthuvel Arigovindan, Sep 02, 2014
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    • "It is therefore preferable to model smooth blur variations and then, to deblur the whole image. Smooth PSF variations can be decomposed on a subspace of PSF[8] [9]. The cost of this modeling increases linearly with the number of basis PSF used. "
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    ABSTRACT: Image deblurring is essential to high resolution imaging and is therefore widely used in astronomy, microscopy or computational photography. While shift-invariant blur is modeled by convolution and leads to fast FFT-based algorithms, shift-variant blurring requires models both accurate and fast. When the point spread function (PSF) varies smoothly across the field, these two opposite objectives can be reached by interpolating from a grid of PSF samples. Several models for smoothly varying PSF co-exist in the literature. We advocate that one of them is both physically-grounded and fast. Moreover, we show that the approximation can be largely improved by tuning the PSF samples and interpolation weights with respect to a given continuous model. This improvement comes without increasing the computational cost of the blurring operator. We illustrate the developed blurring model on a deconvo-lution application in astronomy. Regularized reconstruction with our model leads to large improvements over existing results.
    18th IEEE International Conference on Image Processing, ICIP 2011, Brussels, Belgium, September 11-14, 2011; 09/2011
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    ABSTRACT: In this report, we are interested in blind restoration of optical images that are degraded by a space-variant (SV) blur and corrupted with Poisson noise. For example, blur variation is due to refractive index mismatch in three dimensional fluorescence microscopy or due to atmospheric turbulence in astrophysical images. In our work, the SV Point Spread Function (PSF) is approximated by a convex combination of a set of space-invariant (SI) blurring functions. The problem is thus reduced to the estimation of the set of SI PSFs and the true image. For that, we rely on a Joint Maximum A Posteriori (JMAP) approach where the image and the PSFs are jointly estimated by minimizing a given criterion including l1 and l2 norms for regularizing the image and the PSFs. Our contribution is to provide a functional for the SV blind restoration problem allowing to simultaneously estimate the PSFs and the image. We show the existence of a minimizer of such a functional in the continuous setting. We describe an algorithm based on an alternate minimization scheme using a fast scaled gradient projection (SGP) algorithm. The efficiency of the proposed method is shown on simulated and real images.
    SIAM Journal on Imaging Sciences 10/2014; 7(4). DOI:10.1137/130945776 · 2.27 Impact Factor
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    ABSTRACT: In three-dimensional (3D) computational imaging for wide-field microscopy, estimation methods that solve the inverse imaging problem play an important role. The accuracy of the forward model has a significant impact on the complexity of the estimation method and consequently on the accuracy of the estimated intensity. Previous studies have shown that a forward model based on a depth-varying point-spread function (DV-PSF) leads to a substantial improvement in the resulting images because it accounts for depth-induced aberrations present in the imaging system. In this depth-varying (DV) model, the depth-dependent imaging effects are handled using a stratum-based interpolation method defined on discrete, non-overlapping layers or strata along the Z axis. Recently, a new approximation method based on a principle component analysis (PCA) was developed to predict DV-PSFs1 with improved accuracy over the DV-PSFs predicted by the strata interpolation method of Ref. [11]. In this study, we implemented the PCA-based forward model for DV imaging to further compare the two approaches. DV-PSFs and forward models were computed using both the strata-based and the new PCA-based approximation schemes. Differences are quantified as a function of the approximation, i.e. the number of bases or strata used in each case respectively. A new PCA-based image estimation method was also developed based on the DV expectation maximization (DV-EM) algorithm of Ref. [11]. Preliminary evaluation of the performance of the PCA-based estimation shows promising results and consistency with previous results obtained in previous studies.
    Proceedings of SPIE - The International Society for Optical Engineering 02/2011; 7904. DOI:10.1117/12.875781 · 0.20 Impact Factor
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