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.

Recent developments in spectrum-sharing technologies include integrated sensing and communications (ISAC) systems to save resources, cost, and power. In this paper, we consider a co-existence topology with n-tuple radar and communications transmitters, wherein neither the transmitted signal nor the channels are known. Estimating these unknown quantities is modeled as a n-tuple blind deconvolution problem (NTBD). The receiver is considered to be a uniform linear antenna array. Thus, the channels are modeled as continuous-valued time delay, Doppler modulation, and direction of arrival (DoA). Also, harnessing the sparse nature of the channels and their continuousvalued parametrization, we propose a 3D n-tuple atomic norm minimization (NANM). Casting the NANM problem to its corresponding dual optimization problem, and employing the theory of positive trigonometric polynomial, we formulate a semidefinite program for the estimation of the unknown channel parameters. Performance guarantees of the proposed algorithm are provided in terms of the minimum number of samples required for exact recovery. Finally, numerical simulations validate our theoretical insights.

Due to environmental and economic constraints inherent to seismic exploration, there are often missing shotpoints and receivers that degrade the resolution of the final seismic image. Hence sophisticated interpolation techniques are required for the recovery of dense and uniform spatial sampling. Recent approaches improve the interpolation by adopting robust models through denoisers. We introduce a 3D shot gather interpolation method that jointly considers a sparse prior and a regularization induced by a multichannel volumetric denoiser. The proposed volumetric regularization uses collaborative filters that perform denoising through transform-domain shrinkage of a group of similar seismic cubes extracted from a land seismic acquisition. This grouping and collaborative filtering paradigm exploit the local correlation present in each cube and the non-local correlation between different cubes. Experiments on theStratton 3D surveyshow that the proposed method can interpolate 3D shot gathers in an orthogonal seismic recording from a swath geometry, outperforming methods based on 2D denoisers and 5D seismic data reconstruction in terms of root mean square error and in the recovery of seismic reflections.

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.

We consider a general spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown at the receiver. In this dual-blind deconvolution (DBD) problem, a common receiver admits the multi-carrier wireless communications signal that is overlaid with the radar signal reflected-off multiple targets. When the radar receiver is not collocated with the transmitter, such as in passive or multistatic radars, the transmitted signal is also unknown apart from the target parameters. Similarly, apart from the transmitted messages, the communications channel may also be unknown in dynamic environments such as vehicular networks. As a result, the estimation of unknown target and communications parameters in a DBD scenario is highly challenging. In this work, we exploit the sparsity of the channel to solve DBD by casting it as an atomic norm minimization problem. Our theoretical analyses and numerical experiments demonstrate perfect recovery of continuous-valued range-time and Doppler velocities of multiple targets as well as delay-Doppler communications channel parameters using uniformly-spaced time samples in the dual-blind receiver.

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 imaging using coded apertures (CA) is a powerful technique that can be used to recover depth, light fields, hyperspectral images and other quantities from a single snapshot. The performance of compressive imaging systems based on CAs mostly depends on two factors: the properties of the mask's attenuation pattern, that we refer to as "codification", and the computational techniques used to recover the quantity of interest from the coded snapshot. In this work, we introduce the idea of using time-varying CAs synchronized with spatially varying pixel shutters. We divide the exposure of a sensor into sub-exposures at the beginning of which the CA mask changes and at which the sensor's pixels are simultaneously and individually switched "on" or "off". This is a practically appealing codification as it does not introduce additional optical components other than the already present CA but uses a change in the pixel shutter that can be easily realized electronically. We show that our proposed time-multiplexed coded aperture (TMCA) can be optimized end to end and induces better coded snapshots enabling superior reconstructions in two different applications: compressive light field imaging and hyperspectral imaging. We demonstrate both in simulation and with real captures (taken with prototypes we built) that this codification outperforms the state-of-the-art compressive imaging systems by a large margin in those applications.

In the past years, one common way of enhancing the spatial resolution of a hyperspectral (HS) image has been to fuse it with complementary information coming from multispectral (MS) or panchromatic images. This paper proposes a new method for reconstructing a high-spatial, high-spectral image from measurements acquired after compressed sensing by multiple sensors of different spectral ranges and spatial resolutions, with specific attention to HS and MS compressed images. To solve this problem, we introduce a fusion model based on the linear spectral unmixing model classically used for HS images and investigate an optimization algorithm based on a block coordinate descent strategy. The nonnegative and sum-to-one constraints resulting from the intrinsic physical properties of abundances as well as a total variation penalization are used to regularize this ill-posed inverse problem. Simulation results conducted on realistic compressed HS and MS images show that the proposed algorithm can provide fusion results that are very close to those obtained with uncompressed images, with the advantage of using a significantly reduced number of measurements.

Compressive spectral imagers reduce the number of sampled pixels by coding and combining the spectral information. However, sampling compressed information with simultaneous high spatial and high spectral resolution demands expensive high-resolution sensors. This work introduces a model allowing data from high spatial/low spectral and low spatial/high spectral resolution compressive sensors to be fused. Based on this model, the compressive fusion process is formulated as an inverse problem that minimizes an objective function defined as the sum of a quadratic data fidelity term and smoothness and sparsity regularization penalties. The parameters of the different sensors are optimized and the choice of an appropriate regularization is studied in order to improve the quality of the high resolution reconstructed images. Simulation results conducted on synthetic and real data, with different CS imagers, allow the quality of the proposed fusion method to be appreciated.