### Deconvolution — Making the Most of Fluorescence Microscopy

Deconvolution is one of the most common image-reconstruction tasks that arise in 3D fluorescence microscopy. The aim of this challenge is to benchmark existing deconvolution algorithms and to stimulate the community to look for novel, global and practical approaches to this problem.

The challenge will be divided into two stages: a training phase and a competition (testing) phase. It will primarily be based on realistic-looking synthetic data sets representing various sub-cellular structures. In addition it will rely on a number of common and advanced performance metrics to objectively assess the quality of the results.

# PERFORMANCE METRICS

To assess the quality of the reconstruction we provide several scripts which implement the quality metrics that will be used in the deconvolution challenge. Below we briefly describe these quality metrics and the usage of the corresponding MATLAB scripts.

### Peak Signal-to-Noise Ratio (PSNR)

The PSNR is defined as $$\textrm{PSNR}=10log_{10}(\textrm{peak}^2/\textrm{MSE})$$ where $$\textrm{peak}$$ is the peak value used in the computation and $$\textrm{MSE}$$ is the mean squared error between the reconstruction and the reference image-stack. To compute it we provide the psnr.m script.

## Required Input Arguments

• $$x$$ : Reconstructed image stack (3D MATLAB array).
• $$f$$ : Ground-truth image stack (3D MATLAB array).

## Optional Input Arguments

• $$p$$ : Peak value used in the computation of PSNR (Default: maximum value of $$f$$).

## Output Arguments

• $$\textrm{psnr}$$ : Peak signal to noise ratio.
• $$\textrm{mse}$$ : Minimum mean squared error between $$x$$ and $$f$$.

### Normalized Mean Integrated Squared Error (NMISE)

We use a modified version of the original NMISE metric, which is better suited to the image restoration problem. It is defined as $$\textrm{NMISE}=\frac{1}{N}\sum_{i=1}^N(x_i - f_i)^2/{f_b}_i.$$ To compute it we provide the nmisec.m script.

## Required Input Arguments

• $$x$$ : Reconstructed image stack (3D MATLAB array).
• $$f$$ : Ground-truth image stack (3D MATLAB array).
• $$f_b$$ : Intermediate result, $$f_b=\mathbf{A}\mathbf{x}+\mathbf{b}$$, of the observation model (3D MATLAB array). Output of the ForwardModel3D.m script.

## Output Arguments

• $$\textrm{nmise}$$ : Normalized mean integrated squared error between $$x$$ and $$f$$.

### Structure Similarity Index (SSIM)

The structural similarity (SSIM) index is a metric for measuring the similarity between two images. A description of this metric can be found on Wikipedia. To serve the needs of the 3D reconstruction we provide the ssim3D.m script which can be applied to image volumes.

## Required Input Arguments

• $$x$$ : Reconstructed image stack (3D MATLAB array).
• $$f$$ : Ground-truth image stack (3D MATLAB array).

## Optional Input Arguments

• $$K$$ : constants in the SSIM index formula (see ssim_index.m) (Default : $$K$$ = [0.01 0.03]).
• $$\textrm{window}$$ : local window for statistics (see ssim_index.m). The default window is Gaussian given by window = fspecial('gaussian', 11, 1.5).
• L : dynamic range of the images (Default: maximum value of $$f$$).

## Output Arguments

• $$E$$ : The mean ssim index over all the slices of the image stacks.
• $$M$$ : The minimum ssim index over all the slices of the image stacks.

### Fourier Shell Correlation

The Fourier shell correlation measures the normalized cross-correlation coefficient between two image stacks over corresponding shells in the Fourier space, and is defined as $$\mbox{FSC}\left( r \right)=\frac{\sum_{r_i\in r}\hat{f}_1(r_i)\cdot \hat{f}_2^*(r_i)}{\sqrt{\sum_{r_i\in r}{|\hat{f}_1(r_i)|}^2\cdot\sum_{r_i\in r}{|\hat{f}_2(r_i)|}^2}},$$ where $$\hat{f}_1(r_i), \hat{f}_2(r_i)$$ are the Fourier components of the two image stacks at the given spatial frequency $$r_i$$. To compute it we provide the FourierShellCorrelation.m script.

## Required Input Arguments

• m : Output of the FourierMetricsConstructor.m script.
• $$\hat{f}_1$$ : The Fourier transform of the reconstructed image stack.
• $$\hat{f}_2$$ : The Fourier transform of the ground-truth image stack.

## Output Arguments

• $$\mbox{FSC}$$ : The Fourier shell correlation as defined above.

### Relative Energy Regain

The relative energy regain is a Fourier-based quality metric which measures the recovery of information at a range of absolute spatial frequency. For more informations about this metric we refer to the following article: Heintzmann. Estimating missing information by maximum likelihood deconvolution. Micron 38 (2007) 136-144. To compute it we provide the RelativeEnergyRegain.m script.

## Required Input Arguments

• m : Output of the FourierMetricsConstructor.m script.
• $$\tilde{I}$$ : The Fourier transform of the reconstructed image stack.
• $$\tilde{O}$$ : The Fourier transform of the ground-truth image stack.

## Output Arguments

• $$\mbox{G}_R$$ : The relative energy regain.

# Important Dates

January 6, 2014

#### Beginning of evaluation stage

The evaluation stage of the second edition of the challenge has started.

November 6, 2013

#### Evaluation stage

The official stage of the challenge will last around 2 months.

November/December, 2013