Modeling Point Spread Function in Fluorescence Microscopy With a Sparse Gaussian Mixture: Tradeoff Between Accuracy and Efficiency
| Autor: | Denis K. Samuylov, Prateek Purwar, Gábor Székely, Gregory Paul |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Point spread function
Image formation Deblurring Point source Computer science Gaussian ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION Normal Distribution Bayes Theorem 02 engineering and technology Inverse problem Computer Graphics and Computer-Aided Design symbols.namesake Microscopy Fluorescence 0202 electrical engineering electronic engineering information engineering symbols Image Processing Computer-Assisted 020201 artificial intelligence & image processing Algorithm Image resolution Gaussian network model Software Algorithms |
| Zdroj: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. 28(8) |
| ISSN: | 1941-0042 |
| Popis: | Deblurring is a fundamental inverse problem in bioimaging. It requires modeling the point spread function (PSF), which captures the optical distortions entailed by the image formation process. The PSF limits the spatial resolution attainable for a given microscope. However, recent applications require a higher resolution and have prompted the development of super-resolution techniques to achieve sub-pixel accuracy. This requirement restricts the class of suitable PSF models to analog ones. In addition, deblurring is computationally intensive, hence further requiring computationally efficient models. A custom candidate fitting both the requirements is the Gaussian model. However, this model cannot capture the rich tail structures found in both the theoretical and empirical PSFs. In this paper, we aim at improving the reconstruction accuracy beyond the Gaussian model, while preserving its computational efficiency. We introduce a new class of analog PSF models based on the Gaussian mixtures. The number of Gaussian kernels controls both the modeling accuracy and the computational efficiency of the model: the lower the number of kernels, the lower the accuracy and the higher the efficiency. To explore the accuracy-efficiency tradeoff, we propose a variational formulation of the PSF calibration problem, where a convex sparsity-inducing penalty on the number of Gaussian kernels allows trading accuracy for efficiency. We derive an efficient algorithm based on a fully split formulation of alternating split Bregman. We assess our framework on synthetic and real data, and demonstrate a better reconstruction accuracy in both geometry and photometry in point source localization-a fundamental inverse problem in fluorescence microscopy. |
| Databáze: | OpenAIRE |
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