Compressive Sensing Spectroscopy Using a Residual Convolutional Neural Network

Abstract

Compressive sensing (CS) spectroscopy is well known for developing a compact spectrometer which consists of two parts: compressively measuring an input spectrum and recovering the spectrum using reconstruction techniques. Our goal here is to propose a novel residual convolutional neural network (ResCNN) for reconstructing the spectrum from the compressed measurements. The proposed ResCNN comprises learnable layers and a residual connection between the input and the output of these learnable layers. The ResCNN is trained using both synthetic and measured spectral datasets. The results demonstrate that ResCNN shows better spectral recovery performance in terms of average root mean squared errors (RMSEs) and peak signal to noise ratios (PSNRs) than existing approaches such as the sparse recovery methods and the spectral recovery using CNN. Unlike sparse recovery methods, ResCNN does not require a priori knowledge of a sparsifying basis nor prior information on the spectral features of the dataset. Moreover, ResCNN produces stable reconstructions under noisy conditions. Finally, ResCNN is converged faster than CNN.

Deep Cooperative Spectrum Sensing Based on Residual Neural Network Using Feature Extraction and Random Forest Classifier

“…The input data of ResNet are 2D matrices [N UU × N B ], so the proposed architecture is as follows: (i) initially we have a residual layer composed of a convolutional layer 2D (conv2D), for feature extraction, followed by a batch normalization layer, which aims to make the network faster and more stable during the normalization process, and then the activation function rectified linear unit (ReLu). Then, we have another layer conv2D followed by a layer batch normalization, now, however, we add a Add, H(x) = F(x) + x, which has, in order to calculate the residual of the network, which really must be learned compared to what was already known from the input data, F(x) = H(x) − x, where F(x) is mapping of the learnable layers and x are the input data [34]. Finishing with the ReLu activation function; (ii) the next layer is a max pooling 2D, which aims to reduce the dimensionality of the layer's input data and allow assumptions about the resources contained in the clustered sub-regions [34]; (iii) a second residual layer is applied, where we have a conv2D layer followed by a batch normalization and a ReLu, sequentially another conv2D and batch normalization.…”

“…Then, we have another layer conv2D followed by a layer batch normalization, now, however, we add a Add, H(x) = F(x) + x, which has, in order to calculate the residual of the network, which really must be learned compared to what was already known from the input data, F(x) = H(x) − x, where F(x) is mapping of the learnable layers and x are the input data [34]. Finishing with the ReLu activation function; (ii) the next layer is a max pooling 2D, which aims to reduce the dimensionality of the layer's input data and allow assumptions about the resources contained in the clustered sub-regions [34]; (iii) a second residual layer is applied, where we have a conv2D layer followed by a batch normalization and a ReLu, sequentially another conv2D and batch normalization. All this is in parallel with a conv2D and, also, a batch normalization.…”

“…All this is in parallel with a conv2D and, also, a batch normalization. A Add calculates the residuals between the two batch normalization in parallel, then the activation function ReLu is applied [34]; (iv) the next layer is average pooling 2D, which is a dimensional stair reduction operation that calculates the average value for patches of a feature map [34]; (v) a flatten layer is used for data vectorization; (vi) followed by a dropout layer, which aims to avoid overfitting by randomly setting input units to 0 with a rate frequency at each step during training time; (vii) and finally a layer dense, which is a fully connected layer with activation function softmax, y = e x ∑ e x . Figure 2 presents the complete architecture of the proposed ResNet.…”

GPU-based Implementations of MM Algorithms. Application to Spectroscopy Signal Restoration

“…This was adopted for instance in [15], where dense convolutional neural networks (CNNs) were trained to remove artifacts from high-dimensional NMR signals. Similarly, in [16], a residual convolutional neural network, including CNNs and fully connected layers, is built to perform compressive sensing spectroscopy.…”

Sensor Signal and Information Processing III

“…Compressive sensing (CS) spectroscopy is well known for developing a compact spectrometer that consists of two parts: compressively measuring an input spectrum and recovering the spectrum using reconstruction techniques. Kim et al [ 15 ] have proposed a residual convolutional neural network for reconstructing the spectrum from the compressed measurements. The proposed network comprises learnable layers and a residual connection between the input and the output of these learnable layers.…”