Structured LISTA for Multidimensional Harmonic Retrieval

Learned iterative shrinkage thresholding algorithm (LISTA), which adopts deep learning techniques to optimize algorithm parameters from labeled training data, can be successfully applied to small-scale multidimensional harmonic retrieval (MHR) problems. However, LISTA becomes computationally demanding for large-scale MHR because the matrix size of the learned mutual inhibition matrix exhibits quadratic growth with the signal length. These large matrices consume costly memory/computation resources and require a huge amount of labeled data for training. For MHR problems, the mutual inhibition matrix naturally has a Toeplitz structure, implying the degrees of freedom of the matrix can be reduced from quadratic order to linear order. We thereby propose a structured LISTA-Toeplitz network, which imposes Toeplitz structure on the mutual inhibition matrices and applies linear convolution instead of matrix-vector multiplications in traditional LISTA. Both simulation and field tests for air target detection with radar are carried out to validate the performance of the proposed network. For small-scale MHR problems, LISTA-Toeplitz exhibits close or even better recovery accuracy than traditional LISTA, while the former significantly reduces the network complexity and requires much less training data. For large-scale MHR problems, where LISTA is difficult to implement due to the huge size of the matrices, our proposed LISTA-Toeplitz still enjoys good recovery performance.