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FORWARD-MODEL IMPLEMENTATION

The forward model that we adopt in the deconvolution challenge can be mathematically described as $$ \mathbf{y}=Q\left(P\left(\mathbf{A}\mathbf{x}+\mathbf{b}\right)+\mathbf{w}\right), $$ where \(\mathbf{A}\in\mathrm{R}^{M\times N}\) is a matrix that models the effect of the point spread function (psf) of the microscope, \(P\) is an operation that describes the Poisson noise, \(\mathbf{y}\in\mathrm{R}^M,\mathbf{x}\in\mathrm{R}^N\) are the vectorized versions of the observed and ground-truth image stacks, respectively, \(\mathbf{b}\in\mathrm{R}^M\) is a constant vector which models the image background and \(\mathbf{w}\in\mathrm{R}^M\) represents additive i.i.d Gaussian noise. Finally, \(Q\) is a function which quantizes the final output.

To produce the synthetic degraded measurements according to the above forward model we provide the function ForwardModel3D.m. Below there is a description about the input and output arguments of this script.

Required Input Arguments

• \(x\) : Ground-truth image stack (3D MATLAB array).
• \(h\) : Point spread function (3D MATLAB array).
• \(k\) : Scalar value specifying the maximum photons per voxel for the blurred version of the ground-truth image stack.

Optional Input Arguments

• \(b\) : Scalar value for the background of the image-stack. (Default: 0)
• \(\sigma\) : Standard deviation for the Gaussian noise. (Default: 0)
• \(seed\) : Seed for the random noise generators. (Default: 1)

Output Arguments

• \(y\) : The degraded image stack according to the observation model (3D MATLAB array).
• \(f\) : The normalized ground-truth image stack (3D MATLAB array). The normalization is performed according to the chosen average photons per voxel. This is necessary so as to ensure that the evaluation of the reconstructions is correctly performed. Also note that since the region of interest does not correspond to the full size of the ground-truth image stack, the output is further cropped to match the size of the measurements.
• \(f_b\) : MATLAB 3D array which corresponds to the intermediate result \(\mathbf{A}\mathbf{x}+\mathbf{b}\) of the observation model. This output is used as an input in one of the used quality metrics.

Important Dates