Discrete Laplacian deconvolution for differential interference contrast microscopy

We describe the discrete Laplacian deconvolution (DLD) method for reconstructing an image from its directional derivatives in multiple directions. The DLD models the derivative measurements as discrete convolutions and efficiently computes the ridge regression or the pseudoinverse estimate of the underlying image using the fast Fourier transform. We apply the method to differential interference contrast (DIC) microscopy, and show that under certain conditions, our proposed method is equivalent to the spiral phase integration (SPI) method. Unlike the SPI method, the DLD method can be used with more than two gradient measurement images. We illustrate the use of DLD on both simulated and empirical DIC images, demonstrating image reconstruction performance improvements from using multiple gradient images.