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.

`psnr.m`

script.

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

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

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

`nmisec.m`

script.

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

script.

- \(\textrm{nmise}\) : Normalized mean integrated squared error between \(x\) and \(f\).

`ssim3D.m`

script which can be applied to image volumes.

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

- \(K\) : 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 \(f\)).

- \(E\) : 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.

`TVscore.m`

script.

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

- grid : A \(3\times 1\) vector which consists of the spatial sampling rates in the three dimensions of the image stack. If a different sampling rate is used for every dimension of the volume, then it has to be taken into account for the correct computation of the derivative operators. (Default value : [1 1 1])
- bc : A string which specifies the boundary conditions that will be used in the computation of the derivatives. Available inputs 'reflexive' or 'circular' or 'zero'. (Default: 'reflexive').

- R : The TV score as defined above.

`STensor_score.m`

script.

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

- \(G\) : Smoothing kernel used for the computation of the Structure Tensor. (Default: 3D normalized Gaussian of support 3x3x3).
- grid : A \(3\times 1\) vector which consists of the spatial sampling rates in the three dimensions of the image stack. If a different sampling rate is used for every dimension of the volume, then it has to be taken into account for the correct computation of the derivative operators. (Default value : [1 1 1])
- bc : A string which specifies the boundary conditions that will be used in the computation of the derivatives. Available inputs 'reflexive' or 'circular' or 'zero'. (Default: 'reflexive').

- \(R\) : The Structure Tensor score as defined above.

`Curvature_score.m`

script.

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

- grid : A \(3\times 1\) vector which consists of the spatial sampling rates in the three dimensions of the image stack. If a different sampling rate is used for every dimension of the volume, then it has to be taken into account for the correct computation of the derivative operators. (Default value : [1 1 1])
- bc : A string which specifies the boundary conditions that will be used in the computation of the derivatives. Available inputs 'reflexive' or 'circular' or 'zero'. (Default: 'reflexive').

- \(R\) : The curvature score as defined above.

`wavsparseidx.m`

script.

- \(x\) : Input image stack (3D MATLAB array).
- \(J\) : Decomposition depth of the wavelet transoform.
- \(d\) : A boolean entry which indicates whether we are using a non-redundant (true) or redundant (false) wavelet transform.
- \(f\) : Wavelet family (see
`BiorthWavFilters1D.m`

routine for the available wavelet transforms).

- \(R\) : The wavelet sparsity index of the input.

`FourierShellCorrelation.m`

script.

- 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.

- \(\mbox{FSC}\) : The Fourier shell correlation as defined above.

`RelativeEnergyRegain.m`

script.

- 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.

- \(\mbox{G}_R\) : The relative energy regain.

The training stage of the 2nd edition of the challenge will begin soon. Follow this link for early registration.

July 15, 2013