Deconvolution

The purpose of the image deconvolution module is to correct the blur and remove the noise of the input time lapse. Pinhole PSF and Poisson Blur process need to be reverted. Iterative algorithms are employed to obtain estimates of an ideal image. We use the itk Deconvolution Framework in ITK to restore input time lapse.

We use the PSF functions with PSF Generator Module. Otherwise noticed, the images we employ have been collected with an ZEISS LSM 510 microscope with lens 43x or 60x

Richardson Lucy Deconvolution

Richarson-Lucyis the reference algorithm to restore Poisson degraded images. We use reference implementation in ITK to instantiate different configurations.

TestRichardsonLucyDeconvolution processes the observed time lapse to obtain an unregularized estimate of the original image. Lack of regularization usually has the opposite effect to the desired: noise amplification. Thus it is quite more practical to employ a regularized version.

TestRichardsonLucyL1L2Deconvolution regularizes the Richardson-Lucy update employing a simple Elastic-Net prior. A pure L2 prior produces images with soft transitions among regions, provided diffused estimations of the original image. However, a L1 prior tends to give too sparse solutions are zero coefficients are given to pairs of correlated pixels. The Elastic Net L2 + L1 regularizer provides an intermediate step, as correlated pixels tend to get similar weights in the solution. However, the main image features are usually given by higher order spatial features.

TestRichardsonLucyTVDeconvolution imposes a Total Variation prior on the original images. The TV prior induces images with smooth regions and sharp edges.