Abstract—A deep neural network is used to recognize the nonzero positions of a one-dimensional signal in its sparse domain. Unlike classical data reconstruction methods in compressive sensing (CS), such as basis pursuit or recast as a linear programming problem and solved with primal-dual interior point method (PDIPM), the proposed data reconstruction method is inspired by the performance of convolutional neural networks (CNNs) on image edge detection. A CNN is expected to find the nonzero positions of a sequence in the sparse domain. The proposed method trains the CNN with deep residual learning [1] and takes the half-mean-squared-error (HMSE) as the loss function. It is difficult with a CNN to get accurate amplitude of nonzero points directly, but the CNN finds the nonzero positions efficiently. When the nonzero positions are found, lower–upper (LU) matrix factorization with partial pivoting can be used to acquire accurate CS reconstruction. The experiments show that the proposed method operates with higher speed and reconstruction accuracy than competing methods. 

Index Terms—compressive sensing, CNN, primal-dual interior point, data reconstruction

Cite: Youhao Yu and Richard M. Dansereau, "Fast Reconstruction of 1D Compressive Sensing Data Using a Deep Neural Network," International Journal of Signal Processing Systems, Vol. 8, No. 1, pp. 26-31, March 2020. doi: 10.18178/ijsps.8.1.26-31