PURE-LET Deconvolution of 3D Fluorescence Microscopy Images

 Blurred noisy Deconvolved Three-dimensional (3D) deconvolution microscopy is very effective in improving the quality of fluorescence microscopy images. We present an efficient approach [1] for the deconvolution of 3D fluorescence microscopy images based on the recently developed PURE-LET algorithm [2][3]. Key points: By combining multiple Wiener filtering and wavelet denoising, we parametrize the deconvolution process as a linear combination of elementary functions (LET). Then the Poisson unbiased risk estimate (PURE) is used to obtain the optimal coefficients. The proposed approach is non-iterative and outperforms existing techniques (usually, variants of Richardson-Lucy algorithm) both in terms of computational efficiency and quality. We illustrated its effectiveness on both synthetic and real data.

Simulation results

Algorithm performance is measured in terms of the peak signal-to-noise ratio (PSNR) in dB. All experiments are carried out on a Macbook Pro with a 2.8 GHz Intel Core i7, with 16 GB of RAM.

We perform experiments over two images, Bars and Pollen. The corresponding PSFs with different sizes are generated based on the Gibson-Lanni model [4][5]. They are used to convolve the ground truth images. The blurred images are subsequently contaminated by Poisson noise with different noise levels (corresponding to different $$\alpha$$ values).

 (a) PSF (b) Bars (c) Pollen

Figure 1. Test PSF (Point spread function) and images used for the simulations. (a) $$(x,y)$$ and $$(x,z)$$ sections of one PSF ($$256 \times 256 \times 128$$) based on the Gibson-Lanni model [5]. (b) The Bars image ($$256 \times 256 \times 128$$). (c) The Pollen image ($$256 \times 256 \times 32$$). Image intensity ranges are normalized to the interval [0, 255].

The Bars image

 (a) Original (b) Blurred noisy (c) RL-TV (d) ParalIterDecon (e) MitivDecon (f) PURE-LET

Figure 2. $$(x,y)$$ and $$(y,z)$$ sections of the 3D restoration results of the Bars image with Poisson noise $$\alpha= 0.5$$. (a) and (b) The original image and the blurred noisy image, respectively; (c) RL-TV [6] (PSNR=26.92 dB); (d) ParalIterDecon (PSNR = 26.13 dB); (e) MitivDecon [7] (PSNR=26.41 dB); (f) PURE-LET (PSNR=28.26 dB). The computational time of PURE-LET is 38.02s while other approaches need more than 127.05s.

The Pollen image

 (a) Original (b) Blurred noisy (c) RL-TV (d) ParalIterDecon (e) MitivDecon (f) PURE-LET

Figure 3. $$(x,y)$$ and $$(x,z)$$ sections of the 3D restoration results of the Pollen image with Poisson noise $$\alpha= 1$$. (a) and (b) The original image and the blurred noisy image, respectively; (c) RL-TV [6] (PSNR=27.22 dB); (d) ParalIterDecon (PSNR = 25.58 dB); (e) MitivDecon [7] (PSNR=27.51 dB); (f) PURE-LET (PSNR=28.16 dB). The computational time of PURE-LET is 11.09s while other approaches need more than 27.52s.

Real fluorescence microscopy image

This is the image of microtubules in a Drosophila S2 cell, collected on a Zeiss Elyra super-resolution microscope by Chris Rieken. It consists of one 3D wide field image and a super-resolution Structured Illumination Microscope (SIM) image which can be used for comparison. These images are of size $$256\times 256\times 44$$. The pixel size is then 0.1588 $$\mu$$m. Results are visualized by the Icy software.

 (a) Wide field (b) SIM (c) Deconvolved (d) Wide field (e) SIM (f) Deconvolved

Figure 4. Comparison of the deconvolution result and the super-resolution SIM image on the real data. (a-c) $$(x,y)$$ and $$(x,z)$$ sections of one slice; (d-f) 3D volume visualization (computational time: 21.48seconds).

Compared with the wide field image, the deconvolved image produces a much better quality image, in particular increases the image resolution along the axial direction. Our approach can achieve roughly the same resolution, but with a much faster acquisition time: the SIM technique needs 15 wide field images (with different illuminations) to reconstruct one super-resolution image while our deconvolution approach needs to process just one wide field image.

Conclusion

We proposed a non-iterative and efficient deconvolution approach for 3D fluorescence microscopy images. The proposed PURE-LET approach outperforms current state-of-the-art techniques, both qualitatively and computationally. In addition, the result on real wide field image shows the potential of deconvolution techniques to achieve the super-resolution of Structured Illumination Microscopy. Future work will focus on estimating the PSF automatically from the measurements.

References

• [1] J. Li, F. Luisier and T. Blu, “PURE-LET deconvolution of 3D fluorescence microscopy images”, 2017 14th Proc. IEEE Int. Symp. Biomed. Imaging (ISBI 2017), Melbourne, Australia, 2017, pp. 723-727. [Link] (Best Student Paper Award, 2nd place)

• [2] J. Li, F. Luisier and T. Blu, “PURE-LET image deconvolution”, IEEE Trans. Image Process., 2017, to appear. [Link]

• [3] J. Li, F. Luisier and T. Blu, “Deconvolution of Poissonian images with the PURE-LET approach”, 2016 23rd Proc. IEEE Int. Conf. on Image Processing (ICIP 2016), Phoenix, Arizona, USA, 2016, pp.2708-2712. [Link] (Best Paper Runner-up Award)

• [4] J. Li, F. Xue and T. Blu, “Fast and accurate three-dimensional point spread function computation for fluorescence microscopy”, J. Opt. Soc. Am. A, vol. 34, no. 6, pp. 1029-1034, 2017. [Link] [Demo] [Matlab Code] [ImageJ Plugin]

• [5] S. F. Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy”, J. Opt. Soc. Am. A, vol. 9, no. 1, pp. 154-166, 1992. [Link]

• [6] N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution”, Microsc. Res. Tech., vol. 69, no. 4, pp. 260-266, 2006. [Link]

• [7] Note that MitivDecon is NOT the method in F. Soulez, “A ‘‘learn 2D, apply 3D” method for 3D deconvolution microscopy", ISBI 2014, Beijing, China, 2014, pp. 1075-1078.