Redundant Haar wavelet regularization in sparse-view optical diffraction tomography of microbiological structures

An iterative algorithm for sparse-angle optical diffraction tomography in 2D is proposed, which combines elements of the gridding reconstruction technique with the classical scheme of Fourier data consistency iterations subject to non-negativity constraint, additionally supplemented with gradient-domain and wavelet-domain sparsity constraints. The initial gridding step together with a heuristic replenishment method for convolved data points serves to minimize the Fourier-domain interpolation errors while keeping very low oversampling factors, here 1.375. In the considered 2D case this setting leads to reduction of memory use by factor 2 and faster convergence without sacrificing reconstruction quality when compared to results relying on nearest neighbor mapping. The algorithm is tested numerically in 2D with noiseless synthetic data simulated through the Fourier diffraction theorem in a away that prevents nonphysical wrapping of the projection fields within the detector frame. A modified Shepp-Logan phantom is tested together with a custom phantom created from an integrated phase image of a living cell for a set of 32 and 17 projections in full angle. The results indicate that the combination of TV and wavelet based priors is effective with both types of objects. Also, simultaneous use of the two priors always outperforms each of them applied separately. However, the optimal balance between their parameters can vary significantly with different objects and projection sets.