Quantized neural networks employ reduced precision representations for both weights and activations. This quantization process significantly reduces the memory requirements and computational complexity of the network. Binary Neural Networks (BNNs) are the extreme quantization case, representing values with just one bit. Since the sign function is typically used to map real values to binary values, smooth approximations are introduced to mimic the gradients during error backpropagation. Thus, the mismatch between the forward and backward models corrupts the direction of the gradient causing training inconsistency problems and performance degradation. In contrast to current BNN approaches, we propose to employ a binary periodic (BiPer) function during binarization. Specifically, we use a square wave for the forward pass to obtain the binary values and employ the trigonometric sine function with the same period of the square wave as a differentiable surrogate during the backward pass. We demonstrate that this approach can control the quantization error by using the frequency of the periodic function and improves network performance. Extensive experiments validate the effectiveness of BiPer in benchmark datasets and network architectures, with improvements of up to 1% and 0.69% with respect to state-of-the-art methods in the classification task over CIFAR-10 and ImageNet, respectively. Our code is publicly available at https://github.com/edmav4/BiPer.

Seismic data interpolation of irregularly missing traces plays a crucial role in subsurface imaging, enabling accurate analysis and interpretation throughout the seismic processing workflow. Despite the widespread exploration of deep supervised learning methods for seismic data reconstruction, several challenges remain. Particularly, the requirement for extensive training data and poor domain generalization due to the seismic survey’s variability pose significant issues. To overcome these limitations, this article introduces a deep-learning-based seismic data reconstruction approach that leverages data redundancy. This method involves a two-stage training process. First, an adversarial generative network is trained using synthetic seismic data, enabling the extraction and learning of their primary and local seismic characteristics. Second, a reconstruction network is trained with synthetic data generated by the generative adversarial network (GAN), which dynamically adjusts the distortion level at each epoch to promote feature diversity. This approach enhances the generalization capabilities of the reconstruction network by allowing control over the generation of seismic patterns from the latent space of the GAN, thereby reducing the dependency on large seismic databases. Experimental results on field and synthetic seismic datasets, both pre-stack and post-stack, show that the proposed method outperforms the baseline supervised learning and unsupervised approaches, such as deep seismic prior (DSP) and internal learning (IL), by up to 8 dB of PSNR.

Physical and budget constraints often result in irregular sampling, which complicates accurate subsurface imaging. Pre-processing approaches, such as missing trace or shot interpolation, are typically employed to enhance seismic data in such cases. Recently, deep learning has been used to address the trace interpolation problem at the expense of large amounts of training data to adequately represent typical seismic events. Nonetheless, most research in this area has focused on trace reconstruction, with little attention having been devoted to shot interpolation. Furthermore, existing methods assume regularly spaced receivers/sources failing in approximating seismic data from real (irregular) surveys. This work presents a novel shot gather interpolation approach which uses a continuous coordinate-based representation of the acquired seismic wavefield parameterized by a neural network. The proposed unsupervised approach, which we call coordinate-based seismic interpolation (CoBSI), enables the prediction of specific seismic characteristics in irregular land surveys without using external data during neural network training. Experimental results on real and synthetic 3D data validate the ability of the proposed method to estimate continuous smooth seismic events in the time-space and frequency-wavenumber domains, improving sparsity or low-rank-based interpolation methods.

Physical and budget constraints often result in inadequate sampling for accurate subsurface imaging. Preprocessing approaches, such as missing trace interpolation, are typically employed to enhance seismic data in such cases. The compressed sensing (CS) framework has been applied for modeling missing seismic data, which is estimated by sparsity-based computational algorithms. While existing work mainly focuses on recovering missing traces resulting from receiver subsampling, source subsampling has greater economical advantages, as sources are more expensive than receivers. Moreover, stronger image models different from sparsity have not been explored for source recovery. This work presents a consensus equilibrium (CE) approach to recover missing seismic shots, which enables to incorporate various regularization operators modeling different data priors. Simulation results from a real 3-D land seismic dataset demonstrate that the CE approach provides more accurate estimations of the linear and hyperbolic events in the recovered shots, compared with pure sparsity-based reconstructions.

Compressive spectral imaging (CSI) sensors allow the acquisition of spatial and spectral data using a set of coded projections. The single pixel camera (SPC) is a low-cost CSI architecture capable of sensing high-resolution spectral images, whose potential is diminished by its slow acquisition time due to the large number of required projections. To partially alleviate this issue, dual arm optical systems have been designed such that side information of the scene is captured to guide the reconstruction process. To fully exploit the capabilities of the dual system, the SPC sensing matrix, or equivalently the coding patterns; should be properly designed. Therefore, this work proposes an optimized sensing matrix design for the SPC based on a super-pixel map of the scene, obtained from the side information, such that the number of projections is drastically reduced while the reconstruction quality is improved. Indeed, theoretical analysis based on the restricted isometry property indicates that the error of the reconstruction vanishes when the SPC uses the designed sensing matrix. Simulation and experimental results show that the proposed sensing matrix design improves the reconstruction quality. Specifically, the proposed approach improves image quality in up to 15dB compared with the state of the art sensing matrix designs. Moreover, a fast multi-resolution reconstruction approach is proposed based on the designed matrix, which reduces computation time by two orders of magnitude and does not require an iterative process.

Massive amounts of data in spectral imagery increase acquisition, storing and processing costs. Compressive spectral imaging (CSI) methods allow the reconstruction of spatial and spectral information from a small set of random projections. The single pixel camera is a low cost optical architecture which enables the compressive acquisition of spectral images. Traditional CSI reconstruction methods obtain a sparse approximation of the underlying spatial and spectral information, however the complexity of these algorithms increases in proportion to the dimensionality of the data. This work proposes a multiresolution (MR) CSI reconstruction approach from single pixel camera measurements that exploits spectral similarities between pixels to group them in super-pixels such that the total number of unknowns in the inverse problem is reduced. Specifically, two different types of super-pixels are considered: rectangular and irregular structures. Simulation and experimental results show that the proposed MR scheme improves reconstruction quality in up to 6dB of PSNR and reconstruction time in up to 90% with respect to the traditional full resolution reconstructions.

Compressive spectral imaging captures the spatial and spectral information of a scene using a set of two-dimensional random projections. Compressed sensing reconstruction algorithms are then used to recover the underlying three-dimensional source. This work presents a new generation of devices that attain compressive spectral image measurements by means of a colored-patterned detector and a dispersive element. Simulations show that these new generation devices can recover spectral scenes with up to 5 dB gain in PSNR with respect to traditional Coded Aperture Snapshot Spectral Imaging (CASSI) systems.