caa a22 4500 606199454 CHVBK 20210128100938.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s11045-013-0262-3 doi (NATIONALLICENCE)springer-10.1007/s11045-013-0262-3 A wavelet based method for image reconstruction from gradient data with applications [Elektronische Daten] [Ioana Sevcenco, Peter Hampton, Panajotis Agathoklis] In this paper, an algorithm for image reconstruction from gradient data based on the Haar wavelet decomposition is proposed. The proposed algorithm has two main stages. First, the Haar decomposition of the image to be reconstructed is obtained from the given gradient data set. Then, the Haar wavelet synthesis is employed to produce the image. The proposed algorithm is based on the relationship between the Haar analysis and synthesis filters and the model for the discretized gradient. The approach presented here is based on the one by Hampton et al. (IEEE J Sel Top Signal Process 2(5):781-792, 2008) for wavefront reconstruction in adaptive optics. The main strength of the proposed algorithm lies in its multiresolution nature, which allows efficient processing in the wavelet domain with complexity $${\fancyscript{O}}(N)$$ O ( N ) . In addition, obtaining the wavelet decomposition of the image to be reconstructed provides the possibility for further enhancements of the image, such as denoising or smoothing via iterative Poisson solvers at each resolution during Haar synthesis. To evaluate the performance of the proposed algorithm, it is applied to reconstruct ten standard test images. Experiments demonstrate that the algorithm yields results comparable in terms of solution accuracy to those produced by well-known benchmark algorithms. Further, experiments show that the proposed algorithm is suitable to be employed as a final step to reconstruct an image from a gradient data set, in applications such as image stitching or image morphing. Springer Science+Business Media New York, 2013 Image reconstruction nationallicence Gradient nationallicence Haar decomposition nationallicence Poisson solver nationallicence Sevcenco Ioana Department of Electrical and Computer Engineering, University of Victoria, V8P 5C2, Victoria, BC, Canada aut Hampton Peter 307-720 Eighth Avenue, V3M 2R3, New Westminster, Canada aut Agathoklis Panajotis Department of Electrical and Computer Engineering, University of Victoria, V8P 5C2, Victoria, BC, Canada aut Multidimensional Systems and Signal Processing Springer US; http://www.springer-ny.com 26/3(2015-07-01), 717-737 0923-6082 26:3<717 2015 26 11045 https://doi.org/10.1007/s11045-013-0262-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11045-013-0262-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sevcenco Ioana Department of Electrical and Computer Engineering, University of Victoria, V8P 5C2, Victoria, BC, Canada aut NATIONALLICENCE 700 1- Hampton Peter 307-720 Eighth Avenue, V3M 2R3, New Westminster, Canada aut NATIONALLICENCE 700 1- Agathoklis Panajotis Department of Electrical and Computer Engineering, University of Victoria, V8P 5C2, Victoria, BC, Canada aut NATIONALLICENCE 773 0- Multidimensional Systems and Signal Processing Springer US; http://www.springer-ny.com 26/3(2015-07-01), 717-737 0923-6082 26:3<717 2015 26 11045