A low-rank decomposition-based deconvolution algorithm for rapid volumetric reconstruction of light field μPIV

Light field micro-particle image velocimetry can characterize three-dimensional microflow through the volumetric reconstruction of tracer particle distributions. This can be achieved by light field imaging and volumetric reconstruction techniques such as the Richardson-Lucy deconvolution (RLD) method. However, the convolution operations of RLD are computationally complex due to the laterally shift-variant point spread function (PSF), which significantly lowers the reconstruction efficiency. Thus, a low-rank decomposition-based deconvolution (LRDD) method is proposed to improve the reconstruction efficiency. Through direct deconvolution, the PSF is converted to a point source, eliminating the shift variance and decreasing the number of convolution kernels, thereby reducing the computational complexity of convolution operations. Further, the point source, which is composed of several two-dimensional matrices, is decomposed into one-dimensional kernels through low-rank decomposition for reducing the computational time of convolution operations. The performance of LRDD and RLD is investigated by numerical studies on the volumetric reconstruction. Experiments were carried out in a microchannel to validate the proposed LRDD. Results demonstrated that the reconstruction efficiency of LRDD is above 9 times faster than RLD for the volumetric reconstruction of the tracer particle distribution.