.. .. ,

.. .. Form,

.. .. Conclusion,

, Alternating proximal method for blind video deconvolution 113

.. .. Experimental-results,

.. .. Conclusion,

.. .. ,

.. .. Conclusion,

, Implementation of the proximity operator for kernel estimation

.. .. Experimental-results,

.. .. Conclusion,

, Deinterlacing as a super-resolution problem: interlaced video of four odd and even fields (left)

, An example of three sub-gradients, p.37

, Iterative gradient descent for minimizing a function f . Each generated iterate has a lower cost than its predecessor

. .. , An illustrative example of the Majorize-Minimize strategy: at each iteration n ? N, a tangent majorant q(·, x n ) of f at x n is built and the next iterate x n+1 is defined as the minimizer of q(·, x n ), p.40

, Note that when x n ? ? n ?f (x n ) belongs to C, the iteration reduces to a simple gradient descent step, An illustration of few iteration of the forward-backward algorithm when f is a smooth function and g is the indicator function of a convex set

, 2 SNR values per frame : Degraded (blue diamond), restored (red circle), p.75

, Foreman sequence : Convergence acceleration

. .. , 78 5.5 Comparison between the proposed method and the one based on a primaldual algorithm from [Condat, 2013] in terms of execution time (s.): proposed method with Algorithm 14 (solid thin blue), primal-dual-based method (dashed thick orange)

. .. P-=-53, 7 Foreman sequence: degraded low resolution fields (top), restored high resolution images (bottom), vol.79

, restored high resolution images (bottom), Claire sequence: degraded low resolution fields (top)

, 10 Tachan sequence: degraded low resolution fields (top), restored high resolution images (bottom), vol.81

, Au théâtre ce soir sequence: degraded low resolution fields (top), restored high resolution images (bottom)

, Connected hypergraph of J = 7 nodes and L = 4 hyperedges, p.88

, Hypergraph of J = 7 nodes, C = 4 computing units and

, Global synchronisation process: Transmission of local summations to the next computing unit

, Global synchronisation process: Transmission of averaged blocks to the previous computing unit

, Linear operator A t that extracts the current frame and its neighbors, p.105

, 10} from computing unit c = 2 to computing unit c = 3

, ?{6,7} from computing unit c = 3 to computing unit c = 2, Transmission of averaged images

, Speedup with respect to the number of used cores: proposed method (solid, blue, diamond), linear speedup (dashed, green)

. .. , Execution time of Algorithm 23 steps: local optimization (left), local synchronization (middle), global synchronization (right), p.110

, Foreman sequence: Input degraded images (top) initial SNR = 24.41 dB, associated restored images (bottom) final SNR = 32.04 dB, p.111

, Claire sequence: Input degraded images (top) initial SNR = 24.77 dB, associated restored images (bottom) final SNR = 33.74 dB, p.112

, 1 norm (thick dashed red), 1 / 2 norm (thick solid blue), log-1 norm (thin magenta '?'), Welsch penalty (thin dashed green)

T. Sltv, T. Soot-tv, and -. .. Welsch-tv, Performance in terms of error on kernel identification with respect to the different regularizations and blur kernels, from left to right: TV, p.132

T. Sltv, T. Soot-tv,-log-tv, and W. .. , Performance in terms of SNR with respect to the different regularizations and blur kernels, from left to right: TV

T. Sltv, T. Soot-tv,-log-tv, and W. .. , Performance in terms of MOVIE with respect to the different regularizations and blur kernels, from left to right: TV

. .. , 7 Foreman sequence: images from the degraded sequence (top), corresponding restored images with the best choice of spatial regularizations in terms of SNR (bottom), Identified blur kernels (P = 101) with the different regularization approaches: Tachan (left), vol.137

, corresponding restored images with the best choice of spatial regularizations in terms of SNR (bottom), Claire sequence: images from the degraded sequence (top)

, 10 Tachan sequence: 4-th and 9-th frames from the restored sequences with the best spatial regularizations in non-blind deconvolution, vol.140, p.141

, Au théâtre ce soir sequence: 4-th and 9-th frames from the restored sequences with the best spatial regularizations in non-blind deconvolution, p.142

, from left to right: degraded sequence, restored sequence with TGV, restored sequence with TVSG, restored sequence with log-TV

. .. , Quality of our deinterlacing and deconvolution method, p.75

, Investigated simulation scenarios and the number of images per core in each case

, List of optimization algorithms used for computing the proximity operator with respect to the different convex regularization functions, p.128

, Gap between the best and worst kernel identification scores, p.132

, Regularization parameters used in the blind deconvolution step, p.133

, Performance of the best non-blind deconvolution methods in terms of MOVIE, Performance of the best non-blind deconvolution methods in terms of SNR. 135 7.5

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