A Block Successive Convex Approximation Framework for Multidimensional Harmonic Retrieval and Imperfect Measurements

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In this work we propose a block successive convex approximation algorithm for structured multilinear low-rank tensor decomposition and, more particularly, multidimensional harmonic retrieval for imperfect measurements, where group and rank sparsity is enforced using nuclear norm regularization. Existing optimization algorithms for this non-convex and nondifferentiable optimization problem rely on a lifting approach and a successive convex approximation techniques, which is suitable for implementation on parallel hardware architectures. However, for large scale problems the lifting approach is inefficient and the number of optimization variables increases with the problem dimension. Moreover, using a fully parallelizable algorithm require a large memory capacity to store the whole data set and all the intermediate variables at each iteration. Therefore, we introduce an algorithm, which directly operates on the original parameters space. In this scheme the variable update proceeds sequentially, in a cyclic order leading to a faster convergence to the optimal solution and a reduced complexity in terms of the CPU time and number of iterations.