Efficient phase unwrapping algorithm based on cubature information particle filter applied to unwrap noisy continuous phase maps

This paper presents a new phase unwrapping algorithm for wrapped phase fringes through combining a cubature information particle filter with an efficient local phase gradient estimator and an efficient quality-guided strategy based on heap-sort. The cubature information particle filter that not only is independent from noise statistics but also is not constrained by the nonlinearity of the model constructed is applied to retrieve unambiguous phase from modulus 2π wrapped fringe patterns through constructing a recursive cubature information particle filtering phase unwrapping procedure to perform simultaneously phase unwrapping and noise filtering for the first time to our knowledge, which can be expected to obtain more robust solutions from wrapped phase fringes. Phase gradient estimate is one of the key steps in almost all phase unwrapping algorithms and is directly related to the precision and the efficiency of phase unwrapping procedure. Accordingly, an efficient local phase gradient estimator that is more efficient than ones published previously is deduced to obtain phase gradient information required by the proposed algorithm, which can drastically decrease time consumption of unwrapping procedure and drastically improve the efficiency of the algorithm. The efficient quality-guided strategy based on heap-sort guarantees that the proposed algorithm efficiently unwraps wrapped pixels along the path from the high-reliance regions to the low-reliance regions of wrapped phase images. In addition, the accelerated version of the proposed algorithm is further developed through combing with reversible modulo wavelet operators to solve phase unwrapping problem of wrapped phase images in wavelet transform domain, which can reduce the amount of wrapped pixels that need to be unwrapped, and can further decrease time consumption of unwrapping procedure performing on wrapped phase images. This algorithm and its accelerated version under the frame of wavelet transform are demonstrated with various types of wrapped phase images, showing acceptable solutions.