Background¶
Fluorescence microscopy is a cornerstone of biomedical research. By utilizing fluorescent probes tagged to biological molecules, cellular structures can be visualized under an optical microscope. This information is imperative for investigating biological function as well as biological engineering of molecules for applications like drug development and synthetic biology.
But microscope images are full of noise
Deep learning has been a great tool for denoising, but these methods are typically suited for
Gaussian</b> noise, but microscopy image noise is dominated by signal-dependent Poisson noise. Past methods perform very poorly.
To address this, we incorporate a physics based prior to incorporate the Poisson distribution into the iterations of gradient descent.
$$ p\left(b_i\middle| x\right)=\frac{\left(Ax\right)_i^{b_i}e^{-\left(Ax\right)_i}}{\ b_i!}\ $$These are embedded within a recurrent inference machine (RIM), which produces updates tagged by the gradient of the prior. It combines a RNN with a GRU to gieve the network an internal memory and help it converge faster.
The embedded log gradient is given by:
$$\sum_{i=1}^{M}{{\log{\left(Ax\right)}}_i b_i}-\sum_{i=1}^{M}{{log{\left(Ax\right)}}_i-\sum_{i=1}^{M}log{\left(b_i!\right)}\ \ }$$Training¶
To verify the efficacy of the RIM in cellular fluorescence microscopy, as training set was generated by combining the ground truth images from Biostudies dataset S-BSST265 [14] and the NucleusSegData dataset [15].
This training data represented 86 images containing ~4000 different nuclei. A variety of cell types, fluorescent markers, and magnifications (60-100x) were represented. All images were converted to grayscale and pixel values were scaled between 0 and 1. Training over 50 epochs, we see convergence of the network.
Random amounts of Poisson noise were simulated atop this data where λMax was between .25 and 1. Data augmentation techniques were also included to increase the size of the training data including random horizontal and vertical
We can see over the the time steps, small updates are to restore the images.
We can also see the RIM consistently outperforms other methods. Expectedly, degradation is seen with larger amounts of noise in the input.
With more noise than was present in the training, we see a loss of the image.
Interestingly, we can a strong degree of image reconstruction on non-cell images corrupted with Poisson noise.
