2012/09/04 by Adriana González, Laurent Jacques, Gonzalez, Adriana +5
Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Optical Coherence Tomography Applications #Optical measurement and interference techniques #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging
paper · pdf · doi:10.48550/arxiv.1209.0654
openalex publication_date 2012/09/04 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28
Optical Deflectometric Tomography (ODT) provides an accurate characterization\nof transparent materials whose complex surfaces present a real challenge for\nmanufacture and control. In ODT, the refractive index map (RIM) of a\ntransparent object is reconstructed by measuring light deflection under\nmultiple orientations. We show that this imaging modality can be made\n"compressive", i.e., a correct RIM reconstruction is achievable with far less\nobservations than required by traditional Filtered Back Projection (FBP)\nmethods. Assuming a cartoon-shape RIM model, this reconstruction is driven by\nminimizing the map Total-Variation under a fidelity constraint with the\navailable observations. Moreover, two other realistic assumptions are added to\nimprove the stability of our approach: the map positivity and a frontier\ncondition. Numerically, our method relies on an accurate ODT sensing model and\non a primal-dual minimization scheme, including easily the sensing operator and\nthe proposed RIM constraints. We conclude this paper by demonstrating the power\nof our method on synthetic and experimental data under various compressive\nscenarios. In particular, the compressiveness of the stabilized ODT problem is\ndemonstrated by observing a typical gain of 20 dB compared to FBP at only 5% of\n360 incident light angles for moderately noisy sensing.\n