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This work proposes convolutional-sparse-coded dynamic mode decomposition(CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) andconvolutional sparse coding. EDMD is a data driven analysis method fordescribing a nonlinear dynamical system with a linear time-evolution equation.Compared with existing EDMD methods, CSC-DMD has an advantage of reflectingspatial structure of the target. As an example, the proposed method is appliedto river bed shape estimation from the water surface observation. Theestimation problem is reduced to sparsity-aware restoration with a hardconstraint, which is given by the CSC-DMD prediction, where the algorithm isderived by the primal-dual splitting method. A time series set of water surfaceand bed shape measured through an experimental river setup is used to train andtest the system. From the result, the significance of the proposed method isverified.

Convolutional-Sparse-Coded Dynamic Mode Decomposition and Its Application to River State Estimation