Fast sparse reconstruction algorithm for multidimensional signals

The problem of reconstruction for a sparse multidimensional signal from a multilinear system with separable dictionaries by a limited amount of measurements is addressed. For this aim, a continuous Gaussian function is used to approximate the l₀ norm of a tensor signal, and a steepest ascent algorithm is exploited to optimise the cost function. Compared with the conventional reconstruction techniques, which usually convert the multidimensional signal into a one-dimensional (1D) vector, the proposed method can deal with the multidimensional signal directly, and thus it works fast and saves memory usage. Finally, experimental results of hyperspectral imaging demonstrate that the proposed algorithm can well reconstruct the hyperspectral images with a low computational cost.