sparse recovery algorithm for 3D-localization microscopy

Description

This project involves image deconvolution, filtering, and discrete Fourier transform . We plan to implement an image capture simulator of sparsely-located emitters in three dimensional space and develop a sparse recovery algorithm for 3D-localization microscopy. The simulator and the algorithm will be implemented on MATLAB. The developed algorithm will be characterized based on the simulated images. We also plan to explore another way to improve robustness and localization accuracy of the estimation by following approaches introduced for sparse spike deconvolution [6].

This script simulate a signal (convolution of a few number of spikes and a Gaussian kernel and performs the localization of spikes.

This script simulate a 2D image of a few number of emitters and performs the localization of emitters based on continuous basis pursuit.

References

[1] L. Zhu, W. Zhang, D. Elnatan, and B. Huang, Faster STORM using compressed sensing,” Nature Method, vol. 9, no. 7, pp. 721{723, 2012.
[2] D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, \Quantitative evaluation of software packages for single-molecule localization microscopy,” Nature Method, vol. 12, no. 8, pp. 717{724, 2015.
[3] A. Barsic, G. Grover, and R. Piestun, \Three-dimensional super-resolution and localization of dense clusters of single molecules,” Scienti c Reports, vol. 4, p. 5388, 2014.
[4] F. Heide, W. Heidrich, and G. Wetzstein, \Fast and flexible convolutional sparse coding,” IEEE Conference on Computer Vision and Pattern Recognition, pp. 5135{5143, 2015.
[5] B. Kong and C. C. Fowlkes, \Fast convolutional sparse coding,” tech. rep., Department of Computer Science, University of California, Irvine, 2014.
[6] C. Ekanadham, D. Tranchina, and E. Simoncelli, \Recovery of sparse translation-invariant signals with continuous basis pursuit,” IEEE Transactions on Signal Processing, vol. 59, no. 10, pp. 4735{4744, 2011.

Combination the non-local means and sparse coding approaches to image restoration

Sparse or Collaborative Representation for Face Recognition