Euler's elastica model has a wide range of applications in Image Processing and Computer Vision. However, the non-convexity, the non-smoothness and the nonlinearity of the associated energy functional make its minimization a challenging task, further complicated by the presence of high order derivatives in the model. In this article we propose a new operator-splitting algorithm to minimize the Euler elastica functional. This algorithm is obtained by applying an operator-splitting based time discretization scheme to an initial value problem (dynamical flow) associated with the optimality system (a system of multivalued equations). The sub-problems associated with the three fractional steps of the splitting scheme have either closed form solutions or can be handled by fast dedicated solvers. Compared with earlier approaches relying on ADMM (Alternating Direction Method of Multipliers), the new method has, essentially, only the time discretization step as free parameter to choose, resulting in a very robust and stable algorithm. The simplicity of the sub-problems and its modularity make this algorithm quite efficient. Applications to the numerical solution of smoothing test problems demonstrate the efficiency and robustness of the proposed methodology.
In this paper, we present a Bayes' theorem-based high-speed algorithm, to measure the binary transmission matrix of a multimode fiber using a digital micromirror device, in a reference-less multimode fiber imaging system. Based on conditional probability, we define a preset threshold to locate those digital-micromirror-device pixels that can be switched 'ON' to form a focused spot at the output. This leads to a binary transmission matrix consisting of '0' and '1' elements. High-enhancement-factor light focusing and raster-scanning at the distal end of the fiber are demonstrated experimentally. The key advantage of our algorithm is its capability for fast calibration of a MMF to form a tightly focused spot. In our experiment, for 5000 input-output pairs, we only need 0.26 s to calibrate one row of the transmission matrix to achieve a focused spot with an enhancement factor of 28. This is more than 10 times faster than the prVBEM algorithm. The proposed Bayes' theorem-based binary algorithm can be applied not only in multimode optical fiber focusing but also to other disordered media. Particularly, it will be valuable in fast multimode fiber calibration for endoscopic imaging.
This work demonstrates experimental approaches to characterize a single multimode fiber imaging system without a reference beam. Spatial light modulation is performed with a digital micro-mirror device that enables high-speed binary amplitude modulation. Intensity-only images are recorded by the camera and processed by a Bayesian inference based algorithm to retrieve the phase of the output optical field as well as the transmission matrix of the fiber. The calculated transmission matrix is validated by three standards: prediction accuracy, transmission imaging, and focus generation. Also, it is found that information on mode count and eigenchannels can be extracted from the transmission matrix by singular value decomposition. This paves the way for a more compact and cheaper single multimode fiber imaging system for many demanding imaging tasks.
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