# 3D Deconvolution

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## Description

$\Phi \left ( f \right ) = \sum_{i=1}^{n}\left | g-h * f \right |^{2} + \alpha \cdot \left | f \right |^{2}$

The algorithm is a constrained, iterative approach for solving the L2 regularization of an ill-posed problem to determine the positive fluorescence distribution that minimizes the equation where g is the observed 3-D fluorescence data, f is the underlying 3-dimensional fluorescence distribution, h is the 3-D point-spread function and * denotes convolution. Thus, the algorithm finds the fluorescence distribution that minimizes a weighted combination of the least-squares fit to the observed data (the total squared residuals) and the total squared intensity of the distribution (a measure of "smoothness"), with α the weighting factor that determines the smoothness of the resulting distribution. The software implements an iterative conjugate-gradient method to minimize a related function that has the same minimum, is strictly convex, and is twice differentiable, and the method is guaranteed to converge (Carrington, et al., 1995). Convergence is assumed when the (normalized) first derivative is "small" and the algorithm automatically stops.

## Requirements

• Linux x86_64
• CUDA capable Graphic Card > 1.1
• EPR Library (libepr.so.0.0)
• Big.jar

## EPR Library

EPR Library is available for free to those in academia, as long as the library is only used with uManager. If you need to use the EPR library under other terms, please contact the Biomedical Imaging Group at the University of Massachusetts.

### EPR Library Key

You must obtained a key to use the EPR Library. The key is generated from the email address.

--Karl Bellve, Biomedical Imaging Group, University of Massachusetts 10:36, 22 April 2011 (PDT)