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Chronic wounds pose an ongoing health concern globally, largely due to the prevalence of conditions such as diabetes and leprosy's disease. The standard method of monitoring these wounds involves visual inspection by healthcare professionals, a practice that could present challenges for patients in remote areas with inadequate transportation and healthcare infrastructure. This has led to the development of algorithms designed for the analysis and follow-up of wound images, which perform image-processing tasks such as classification, detection, and segmentation. However, the effectiveness of these algorithms heavily depends on the availability of comprehensive and varied wound image data, which is usually scarce. This paper introduces the CO2Wounds-V2 dataset, an extended collection of RGB wound images from leprosy patients with their corresponding semantic segmentation annotations, aiming to enhance the development and testing of image-processing algorithms in the medical field., Comment: 2024 IEEE International Conference on Image Processing (ICIP 2024)

Seismic data frequently exhibits missing traces, substantially affecting subsequent seismic processing and interpretation. Deep learning-based approaches have demonstrated significant advancements in reconstructing irregularly missing seismic data through supervised and unsupervised methods. Nonetheless, substantial challenges remain, such as generalization capacity and computation time cost during the inference. Our work introduces a reconstruction method that uses a pre-trained generative diffusion model for image synthesis and incorporates Deep Image Prior (DIP) to maintain data consistency when reconstructing missing traces in seismic images. The proposed method has demonstrated strong robustness and high reconstruction capability for field and synthetic seismic images with different levels of structural complexity, even in scenarios where test images were outside the training domain. This indicates that our method can handle the high geological variability of different exploration targets. Additionally, compared to other state-of-the-art seismic reconstruction methods using diffusion models, our approach reduces the number of neural function evaluations by up to 4x., Comment: 5 pages, 4 figures, 3 tables. Submitted to geoscience and remote sensing letters

Computational optical imaging (COI) systems have enabled the acquisition of high-dimensional signals through optical coding elements (OCEs). OCEs encode the high-dimensional signal in one or more snapshots, which are subsequently decoded using computational algorithms. Currently, COI systems are optimized through an end-to-end (E2E) approach, where the OCEs are modeled as a layer of a neural network and the remaining layers perform a specific imaging task. However, the performance of COI systems optimized through E2E is limited by the physical constraints imposed by these systems. This paper proposes a knowledge distillation (KD) framework for the design of highly physically constrained COI systems. This approach employs the KD methodology, which consists of a teacher-student relationship, where a high-performance, unconstrained COI system (the teacher), guides the optimization of a physically constrained system (the student) characterized by a limited number of snapshots. We validate the proposed approach, using a binary coded apertures single pixel camera for monochromatic and multispectral image reconstruction. Simulation results demonstrate the superiority of the KD scheme over traditional E2E optimization for the designing of highly physically constrained COI systems., Comment: 7 pages, 3 figures. Accepted at ICIP 2024

Deep-learning (DL)-based image deconvolution (ID) has exhibited remarkable recovery performance, surpassing traditional linear methods. However, unlike traditional ID approaches that rely on analytical properties of the point spread function (PSF) to achieve high recovery performance - such as specific spectrum properties or small conditional numbers in the convolution matrix - DL techniques lack quantifiable metrics for evaluating PSF suitability for DL-assisted recovery. Aiming to enhance deconvolution quality, we propose a metric that employs a non-linear approach to learn the invertibility of an arbitrary PSF using a neural network by mapping it to a unit impulse. A lower discrepancy between the mapped PSF and a unit impulse indicates a higher likelihood of successful inversion by a DL network. Our findings reveal that this metric correlates with high recovery performance in DL and traditional methods, thereby serving as an effective regularizer in deconvolution tasks. This approach reduces the computational complexity over conventional condition number assessments and is a differentiable process. These useful properties allow its application in designing diffractive optical elements through end-to-end (E2E) optimization, achieving invertible PSFs, and outperforming the E2E baseline framework., Comment: Accepted at EUSIPCO 2024

Binary Neural Networks emerged as a cost-effective and energy-efficient solution for computer vision tasks by binarizing either network weights or activations. However, common binary activations, such as the Sign activation function, abruptly binarize the values with a single threshold, losing fine-grained details in the feature outputs. This work proposes an activation that applies multiple thresholds following dithering principles, shifting the Sign activation function for each pixel according to a spatially periodic threshold kernel. Unlike literature methods, the shifting is defined jointly for a set of adjacent pixels, taking advantage of spatial correlations. Experiments over the classification task demonstrate the effectiveness of the designed dithering Sign activation function as an alternative activation for binary neural networks, without increasing the computational cost. Further, DeSign balances the preservation of details with the efficiency of binary operations., Comment: 7 pages

In the era of cloud computing and data-driven applications, it is crucial to protect sensitive information to maintain data privacy, ensuring truly reliable systems. As a result, preserving privacy in deep learning systems has become a critical concern. Existing methods for privacy preservation rely on image encryption or perceptual transformation approaches. However, they often suffer from reduced task performance and high computational costs. To address these challenges, we propose a novel Privacy-Preserving framework that uses a set of deformable operators for secure task learning. Our method involves shuffling pixels during the analog-to-digital conversion process to generate visually protected data. Those are then fed into a well-known network enhanced with deformable operators. Using our approach, users can achieve equivalent performance to original images without additional training using a secret key. Moreover, our method enables access control against unauthorized users. Experimental results demonstrate the efficacy of our approach, showcasing its potential in cloud-based scenarios and privacy-sensitive applications., Comment: copyright 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

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.

The modern surge in camera usage alongside widespread computer vision technology applications poses significant privacy and security concerns. Current artificial intelligence (AI) technologies aid in recognizing relevant events and assisting in daily tasks in homes, offices, hospitals, etc. The need to access or process personal information for these purposes raises privacy concerns. While software-level solutions like face de-identification provide a good privacy/utility trade-off, they present vulnerabilities to sniffing attacks. In this paper, we propose a hardware-level face de-identification method to solve this vulnerability. Specifically, our approach first learns an optical encoder along with a regression model to obtain a face heatmap while hiding the face identity from the source image. We also propose an anonymization framework that generates a new face using the privacy-preserving image, face heatmap, and a reference face image from a public dataset as input. We validate our approach with extensive simulations and hardware experiments., Comment: Accepted to CVPR 2024. Project Website and Code coming soon

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 still remain open. Particularly, the requirement of extensive training data and poor domain generalization due to the seismic survey's variability poses significant issues. To overcome these limitations, this paper 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 (GAN) 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 GAN, which dynamically adjusts the noise and 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 and internal learning, by up to 8 dB of PSNR., Comment: 11 pages, 11 figures

Integrated sensing and communications (ISAC) systems have gained significant interest because of their ability to jointly and efficiently access, utilize, and manage the scarce electromagnetic spectrum. The co-existence approach toward ISAC focuses on the receiver processing of overlaid radar and communications signals coming from independent transmitters. A specific ISAC coexistence problem is dual-blind deconvolution (DBD), wherein the transmit signals and channels of both radar and communications are unknown to the receiver. Prior DBD works ignore the evolution of the signal model over time. In this work, we consider a dynamic DBD scenario using a linear state space model (LSSM) such that, apart from the transmit signals and channels of both systems, the LSSM parameters are also unknown. We employ a factor graph representation to model these unknown variables. We avoid the conventional matrix inversion approach to estimate the unknown variables by using an efficient expectation-maximization algorithm, where each iteration employs a Gaussian message passing over the factor graph structure. Numerical experiments demonstrate the accurate estimation of radar and communications channels, including in the presence of noise., Comment: 13 pages, 4 figures

Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the phase retrieval (PR) problem, wherein a complex-valued signal is estimated through its intensity-only projections, has attracted significant interest. The hypercomplex PR (HPR) arises in many optical imaging and computational sensing applications that usually comprise quaternion and octonion-valued signals. Analogous to the traditional PR, measurements in HPR may involve complex, hypercomplex, Fourier, and other sensing matrices. This set of problems opens opportunities for developing novel HSP tools and algorithms. This article provides a synopsis of the emerging areas and applications of HPR with a focus on optical imaging., Comment: 10 pages, 4 figures, 2 tables

Depth estimation from a single image of a conventional camera is a challenging task since depth cues are lost during the acquisition process. State-of-the-art approaches improve the discrimination between different depths by introducing a binary-coded aperture (CA) in the lens aperture that generates different coded blur patterns at different depths. Color-coded apertures (CCA) can also produce color misalignment in the captured image which can be utilized to estimate disparity. Leveraging advances in deep learning, more recent works have explored the data-driven design of a diffractive optical element (DOE) for encoding depth information through chromatic aberrations. However, compared with binary CA or CCA, DOEs are more expensive to fabricate and require high-precision devices. Different from previous CCA-based approaches that employ few basic colors, in this work we propose a CCA with a greater number of color filters and richer spectral information to optically encode relevant depth information in a single snapshot. Furthermore, we propose to jointly learn the color-coded aperture (CCA) pattern and a convolutional neural network (CNN) to retrieve depth information by using an end-to-end optimization approach. We demonstrate through different experiments on three different data sets that the designed color-encoding has the potential to remove depth ambiguities and provides better depth estimates compared to state-of-the-art approaches. Additionally, we build a low-cost prototype of our CCA using a photographic film and validate the proposed approach in real scenarios.

Signal processing over hypercomplex numbers arises in many optical imaging applications. In particular, spectral image or color stereo data are often processed using octonion algebra. Recently, the eight-band multispectral image phase recovery has gained salience, wherein it is desired to recover the eight bands from the phaseless measurements. In this paper, we tackle this hitherto unaddressed hypercomplex variant of the popular phase retrieval (PR) problem. We propose octonion Wirtinger flow (OWF) to recover an octonion signal from its intensity-only observation. However, contrary to the complex-valued Wirtinger flow, the non-associative nature of octonion algebra and the consequent lack of octonion derivatives make the extension to OWF non-trivial. We resolve this using the pseudo-real-matrix representation of octonion to perform the derivatives in each OWF update. We demonstrate that our approach recovers the octonion signal up to a right-octonion phase factor. Numerical experiments validate OWF-based PR with high accuracy under both noiseless and noisy measurements., Comment: 5 pages, 3 figures

Data augmentation is classically used to improve the overall performance of deep learning models. It is, however, challenging in the case of medical applications, and in particular for multiparametric datasets. For example, traditional geometric transformations used in several applications to generate synthetic images can modify in a non-realistic manner the patients' anatomy. Therefore, dedicated image generation techniques are necessary in the medical field to, for example, mimic a given pathology realistically. This paper introduces a new data augmentation architecture that generates synthetic multiparametric (T1 arterial, T1 portal, and T2) magnetic resonance images (MRI) of massive macrotrabecular subtype hepatocellular carcinoma with their corresponding tumor masks through a generative deep learning approach. The proposed architecture creates liver tumor masks and abdominal edges used as input in a Pix2Pix network for synthetic data creation. The method's efficiency is demonstrated by training it on a limited multiparametric dataset of MRI triplets from $89$ patients with liver lesions to generate $1,000$ synthetic triplets and their corresponding liver tumor masks. The resulting Frechet Inception Distance score was $86.55$. The proposed approach was among the winners of the 2021 data augmentation challenge organized by the French Society of Radiology., Comment: Accepted at IEEE ISBI 2023

In recent years, fast technological advancements have led to the development of high-quality software and hardware, revolutionizing various industries such as the economy, health, industry, and agriculture. Specifically, applying information and communication technology (ICT) tools and the Internet of Things (IoT) in agriculture has improved productivity through sustainable food cultivation and environment preservation via efficient use of land and knowledge. However, limited access, high costs, and lack of training have created a considerable gap between farmers and ICT tools in some countries, e.g., Colombia. To address these challenges, we present AgroTIC, a smartphone-based application for agriculture that bridges the gap between farmers, agronomists, and merchants via ubiquitous technology and low-cost smartphones. AgroTIC enables farmers to monitor their crop health with the assistance of agronomists, image processing, and deep learning. Furthermore, when farmers are ready to market their agricultural products, AgroTIC provides a platform to connect them with merchants. We present a case study of the AgroTIC app among citrus fruit farmers from the Santander department in Colombia. Our study included over 200 farmers from more than 130 farms, and AgroTIC positively impacted their crop quality and production. The AgroTIC app was downloaded over 120 times during the study, and more than 170 farmers, agronomists, and merchants actively used the application.

Deep learning methods are state-of-the-art for spectral image (SI) computational tasks. However, these methods are constrained in their performance since available datasets are limited due to the highly expensive and long acquisition time. Usually, data augmentation techniques are employed to mitigate the lack of data. Surpassing classical augmentation methods, such as geometric transformations, GANs enable diverse augmentation by learning and sampling from the data distribution. Nevertheless, GAN-based SI generation is challenging since the high-dimensionality nature of this kind of data hinders the convergence of the GAN training yielding to suboptimal generation. To surmount this limitation, we propose low-dimensional GAN (LD-GAN), where we train the GAN employing a low-dimensional representation of the {dataset} with the latent space of a pretrained autoencoder network. Thus, we generate new low-dimensional samples which are then mapped to the SI dimension with the pretrained decoder network. Besides, we propose a statistical regularization to control the low-dimensional representation variance for the autoencoder training and to achieve high diversity of samples generated with the GAN. We validate our method LD-GAN as data augmentation strategy for compressive spectral imaging, SI super-resolution, and RBG to spectral tasks with improvements varying from 0.5 to 1 [dB] in each task respectively. We perform comparisons against the non-data augmentation training, traditional DA, and with the same GAN adjusted and trained to generate the full-sized SIs. The code of this paper can be found in https://github.com/romanjacome99/LD_GAN.git, Comment: This paper was accepted at the LatinX in Computer Vision Research Workshop at CVPR2023

In joint radar-communications (JRC) applications such as secure military receivers, often the radar and communications signals are overlaid in the received signal. In these passive listening outposts, the signals and channels of both radar and communications are unknown to the receiver. The ill-posed problem of recovering all signal and channel parameters from the overlaid signal is termed as \textit{dual-blind deconvolution} (DBD). In this work, we investigate DBD for a multi-antenna receiver. We model the radar and communications channels with a few (sparse) \textit{continuous-valued} parameters such as time delays, Doppler velocities, and directions-of-arrival (DoAs). To solve this highly ill-posed DBD, we propose to minimize the sum of multivariate atomic norms (SoMAN) that depend on unknown parameters. To this end, we devise an exact semidefinite program using theories of positive hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show that the minimum number of samples and antennas required for perfect recovery is logarithmically dependent on the maximum of the number of radar targets and communications paths rather than their sum. We show that our approach is easily generalized to include several practical issues such as gain/phase errors and additive noise. Numerical experiments show the exact parameter recovery for different JRC scenarios., Comment: 30 pages, 7 figures

Spectral imaging collects and processes information along spatial and spectral coordinates quantified in discrete voxels, which can be treated as a 3D spectral data cube. The spectral images (SIs) allow identifying objects, crops, and materials in the scene through their spectral behavior. Since most spectral optical systems can only employ 1D or maximum 2D sensors, it is challenging to directly acquire the 3D information from available commercial sensors. As an alternative, computational spectral imaging (CSI) has emerged as a sensing tool where the 3D data can be obtained using 2D encoded projections. Then, a computational recovery process must be employed to retrieve the SI. CSI enables the development of snapshot optical systems that reduce acquisition time and provide low computational storage costs compared to conventional scanning systems. Recent advances in deep learning (DL) have allowed the design of data-driven CSI to improve the SI reconstruction or, even more, perform high-level tasks such as classification, unmixing, or anomaly detection directly from 2D encoded projections. This work summarises the advances in CSI, starting with SI and its relevance; continuing with the most relevant compressive spectral optical systems. Then, CSI with DL will be introduced, and the recent advances in combining the physical optical design with computational DL algorithms to solve high-level tasks.

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.

Recent interest in integrated sensing and communications has led to the design of novel signal processing techniques to recover information from an overlaid radar-communications signal. Here, we focus on a spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown to the common receiver. In this dual-blind deconvolution (DBD) problem, the receiver admits a multi-carrier wireless communications signal that is overlaid with the radar signal reflected off multiple targets. The communications and radar channels are represented by continuous-valued range-times or delays corresponding to multiple transmission paths and targets, respectively. Prior works addressed recovery of unknown channels and signals in this ill-posed DBD problem through atomic norm minimization but contingent on individual minimum separation conditions for radar and communications channels. In this paper, we provide an optimal joint separation condition using extremal functions from the Beurling-Selberg interpolation theory. Thereafter, we formulate DBD as a low-rank modified Hankel matrix retrieval and solve it via nuclear norm minimization. We estimate the unknown target and communications parameters from the recovered low-rank matrix using multiple signal classification (MUSIC) method. We show that the joint separation condition also guarantees that the underlying Vandermonde matrix for MUSIC is well-conditioned. Numerical experiments validate our theoretical findings., Comment: 5 pages, 3 figures

This paper proposes a non-data-driven deep neural network for spectral image recovery problems such as denoising, single hyperspectral image super-resolution, and compressive spectral imaging reconstruction. Unlike previous methods, the proposed approach, dubbed Mixture-Net, implicitly learns the prior information through the network. Mixture-Net consists of a deep generative model whose layers are inspired by the linear and non-linear low-rank mixture models, where the recovered image is composed of a weighted sum between the linear and non-linear decomposition. Mixture-Net also provides a low-rank decomposition interpreted as the spectral image abundances and endmembers, helpful in achieving remote sensing tasks without running additional routines. The experiments show the MixtureNet effectiveness outperforming state-of-the-art methods in recovery quality with the advantage of architecture interpretability.

The abundant spatial and angular information from light fields has allowed the development of multiple disparity estimation approaches. However, the acquisition of light fields requires high storage and processing cost, limiting the use of this technology in practical applications. To overcome these drawbacks, the compressive sensing (CS) theory has allowed the development of optical architectures to acquire a single coded light field measurement. This measurement is decoded using an optimization algorithm or deep neural network that requires high computational costs. The traditional approach for disparity estimation from compressed light fields requires first recovering the entire light field and then a post-processing step, thus requiring long times. In contrast, this work proposes a fast disparity estimation from a single compressed measurement by omitting the recovery step required in traditional approaches. Specifically, we propose to jointly optimize an optical architecture for acquiring a single coded light field snapshot and a convolutional neural network (CNN) for estimating the disparity maps. Experimentally, the proposed method estimates disparity maps comparable with those obtained from light fields reconstructed using deep learning approaches. Furthermore, the proposed method is 20 times faster in training and inference than the best method that estimates the disparity from reconstructed light fields.

The increasingly crowded spectrum has spurred the design of joint radar-communications systems that share hardware resources and efficiently use the radio frequency spectrum. We study 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 a multi-carrier wireless communications signal that is overlaid with the radar signal reflected off multiple targets. The communications and radar channels are represented by continuous-valued range-time and Doppler velocities of multiple transmission paths and multiple targets. We exploit the sparsity of both channels to solve the highly ill-posed DBD problem by casting it into a sum of multivariate atomic norms (SoMAN) minimization. We devise a semidefinite program to estimate the unknown target and communications parameters using the theories of positive-hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show that the minimum number of samples required for near-perfect recovery is dependent on the logarithm of the maximum of number of radar targets and communications paths rather than their sum. We show that our SoMAN method and PhTP formulations are also applicable to more general scenarios such as unsynchronized transmission, the presence of noise, and multiple emitters. Numerical experiments demonstrate great performance enhancements during parameter recovery under different scenarios., Comment: 26 pages, 13 figures, 1 table

Computational optical imaging (COI) systems leverage optical coding elements (CE) in their setups to encode a high-dimensional scene in a single or multiple snapshots and decode it by using computational algorithms. The performance of COI systems highly depends on the design of its main components: the CE pattern and the computational method used to perform a given task. Conventional approaches rely on random patterns or analytical designs to set the distribution of the CE. However, the available data and algorithm capabilities of deep neural networks (DNNs) have opened a new horizon in CE data-driven designs that jointly consider the optical encoder and computational decoder. Specifically, by modeling the COI measurements through a fully differentiable image formation model that considers the physics-based propagation of light and its interaction with the CEs, the parameters that define the CE and the computational decoder can be optimized in an end-to-end (E2E) manner. Moreover, by optimizing just CEs in the same framework, inference tasks can be performed from pure optics. This work surveys the recent advances on CE data-driven design and provides guidelines on how to parametrize different optical elements to include them in the E2E framework. Since the E2E framework can handle different inference applications by changing the loss function and the DNN, we present low-level tasks such as spectral imaging reconstruction or high-level tasks such as pose estimation with privacy preserving enhanced by using optimal task-based optical architectures. Finally, we illustrate classification and 3D object recognition applications performed at the speed of the light using all-optics DNN.

We consider a joint multiple-antenna radar-communications system in a co-existence scenario. Contrary to conventional applications, wherein at least the radar waveform and communications channel are known or estimated \textit{a priori}, we investigate the case when the channels and transmit signals of both systems are unknown. In radar applications, this problem arises in multistatic or passive systems, where transmit signal is not known. Similarly, highly dynamic vehicular or mobile communications may render prior estimates of wireless channel unhelpful. In particular, the radar signal reflected-off multiple targets is overlaid with the multi-carrier communications signal. In order to extract the unknown continuous-valued target parameters (range, Doppler velocity, and direction-of-arrival) and communications messages, we formulate the problem as a sparse dual-blind deconvolution and solve it using atomic norm minimization. Numerical experiments validate our proposed approach and show that precise estimation of continuous-valued channel parameters, radar waveform, and communications messages is possible up to scaling ambiguities., Comment: 5 pages, 3 figures

The accelerated use of digital cameras prompts an increasing concern about privacy and security, particularly in applications such as action recognition. In this paper, we propose an optimizing framework to provide robust visual privacy protection along the human action recognition pipeline. Our framework parameterizes the camera lens to successfully degrade the quality of the videos to inhibit privacy attributes and protect against adversarial attacks while maintaining relevant features for activity recognition. We validate our approach with extensive simulations and hardware experiments., Comment: Oral paper presented at European Conference on Computer Vision (ECCV) 2022, in Tel Aviv, Israel

Compressive spectral imaging (CSI) has emerged as an attractive compression and sensing technique, primarily to sense spectral regions where traditional systems result in highly costly such as in the near-infrared spectrum. Recently, it has been shown that spectral classification can be performed directly in the compressive domain, considering the amount of spectral information embedded in the measurements, skipping the reconstruction step. Consequently, the classification quality directly depends on the set of coding patterns employed in the sensing step. Therefore, this work proposes an end-to-end approach to jointly design the coding patterns used in CSI and the network parameters to perform spectral classification directly from the embedded near-infrared compressive measurements. Extensive simulation on the three-dimensional coded aperture snapshot spectral imaging (3D-CASSI) system validates that the proposed design outperforms traditional and random design in up to 10% of classification accuracy., Comment: 5 pages, 5 figures

Compressive spectral imaging (CSI) has attracted significant attention since it employs synthetic apertures to codify spatial and spectral information, sensing only 2D projections of the 3D spectral image. However, these optical architectures suffer from a trade-off between the spatial and spectral resolution of the reconstructed image due to technology limitations. To overcome this issue, compressive spectral image fusion (CSIF) employs the projected measurements of two CSI architectures with different resolutions to estimate a high-spatial high-spectral resolution. This work presents the fusion of the compressive measurements of a low-spatial high-spectral resolution coded aperture snapshot spectral imager (CASSI) architecture and a high-spatial low-spectral resolution multispectral color filter array (MCFA) system. Unlike previous CSIF works, this paper proposes joint optimization of the sensing architectures and a reconstruction network in an end-to-end (E2E) manner. The trainable optical parameters are the coded aperture (CA) in the CASSI and the colored coded aperture in the MCFA system, employing a sigmoid activation function and regularization function to encourage binary values on the trainable variables for an implementation purpose. Additionally, an unrolling-based network inspired by the alternating direction method of multipliers (ADMM) optimization is formulated to address the reconstruction step and the acquisition systems design jointly. Finally, a spatial-spectral inspired loss function is employed at the end of each unrolling layer to increase the convergence of the unrolling network. The proposed method outperforms previous CSIF methods, and experimental results validate the method with real measurements., Comment: 12 pages, 11 figures

Deep learning models are state-of-the-art in compressive spectral imaging (CSI) recovery. These methods use a deep neural network (DNN) as an image generator to learn non-linear mapping from compressed measurements to the spectral image. For instance, the deep spectral prior approach uses a convolutional autoencoder network (CAE) in the optimization algorithm to recover the spectral image by using a non-linear representation. However, the CAE training is detached from the recovery problem, which does not guarantee optimal representation of the spectral images for the CSI problem. This work proposes a joint non-linear representation and recovery network (JR2net), linking the representation and recovery task into a single optimization problem. JR2net consists of an optimization-inspired network following an ADMM formulation that learns a non-linear low-dimensional representation and simultaneously performs the spectral image recovery, trained via the end-to-end approach. Experimental results show the superiority of the proposed method with improvements up to 2.57 dB in PSNR and performance around 2000 times faster than state-of-the-art methods.

The ability of a radar to discriminate in both range and Doppler velocity is completely characterized by the ambiguity function (AF) of its transmit waveform. Mathematically, it is obtained by correlating the waveform with its Doppler-shifted and delayed replicas. We consider the inverse problem of designing a radar transmit waveform that satisfies the specified AF magnitude. This process may be viewed as a signal reconstruction with some variation of phase retrieval methods. We provide a trust-region algorithm that minimizes a smoothed non-convex least-squares objective function to iteratively recover the underlying signal-of-interest for either time- or band-limited support. The method first approximates the signal using an iterative spectral algorithm and then refines the attained initialization based on a sequence of gradient iterations. Our theoretical analysis shows that unique signal reconstruction is possible using signal samples no more than thrice the number of signal frequencies or time samples. Numerical experiments demonstrate that our method recovers both time- and band-limited signals from sparsely and randomly sampled, noisy, and noiseless AFs., Comment: 40 pages, 13 figures, 1 table

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 \textit{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., Comment: 5 pages, 2 figures, submitted to ICASSP 2022

Covering from photography to depth and spectral estimation, diverse computational imaging (CI) applications benefit from the versatile modulation of coded apertures (CAs). The light wave fields as space, time, or spectral can be modulated to obtain projected encoded information at the sensor that is then decoded by efficient methods, such as the modern deep learning decoders. Despite the CA can be fabricated to produce an analog modulation, a binary CA is mostly preferred since easier calibration, higher speed, and lower storage are achieved. As the performance of the decoder mainly depends on the structure of the CA, several works optimize the CA ensembles by customizing regularizers for a particular application without considering critical physical constraints of the CAs. This work presents an end-to-end (E2E) deep learning-based optimization of CAs for CI tasks. The CA design method aims to cover a wide range of CI problems easily changing the loss function of the deep approach. The designed loss function includes regularizers to fulfill the widely used sensing requirements of the CI applications. Mainly, the regularizers can be selected to optimize the transmittance, the compression ratio, and the correlation between measurements, while a binary CA solution is encouraged, and the performance of the CI task is maximized in applications such as restoration, classification, and semantic segmentation.

Accurate land cover segmentation of spectral images is challenging and has drawn widespread attention in remote sensing due to its inherent complexity. Although significant efforts have been made for developing a variety of methods, most of them rely on supervised strategies. Subspace clustering methods, such as Sparse Subspace Clustering (SSC), have become a popular tool for unsupervised learning due to their high performance. However, the computational complexity of SSC methods prevents their use on large spectral remotely sensed datasets. Furthermore, since SSC ignores the spatial information in the spectral images, its discrimination capability is limited, hampering the clustering results' spatial homogeneity. To address these two relevant issues, in this paper, we propose a fast algorithm that obtains a sparse representation coefficient matrix by first selecting a small set of pixels that best represent their neighborhood. Then, it performs spatial filtering to enforce the connectivity of neighboring pixels and uses fast spectral clustering to get the final segmentation. Extensive simulations with our method demonstrate its effectiveness in land cover segmentation, obtaining remarkable high clustering performance compared with state-of-the-art SSC-based algorithms and even novel unsupervised-deep-learning-based methods. Besides, the proposed method is up to three orders of magnitude faster than SSC when clustering more than $2 \times 10^4$ spectral pixels.

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 on real captures (taken with prototypes we built) that this codification outperforms the state-of-the-art compressive imaging systems by more than 4dB in those applications.

In remote sensing, hyperspectral (HS) and multispectral (MS) image fusion have emerged as a synthesis tool to improve the data set resolution. However, conventional image fusion methods typically degrade the performance of the land cover classification. In this paper, a feature fusion method from HS and MS images for pixel-based classification is proposed. More precisely, the proposed method first extracts spatial features from the MS image using morphological profiles. Then, the feature fusion model assumes that both the extracted morphological profiles and the HS image can be described as a feature matrix lying in different subspaces. An algorithm based on combining alternating optimization (AO) and the alternating direction method of multipliers (ADMM) is developed to solve efficiently the feature fusion problem. Finally, extensive simulations were run to evaluate the performance of the proposed feature fusion approach for two data sets. In general, the proposed approach exhibits a competitive performance compared to other feature extraction methods., Comment: 4 pages, 2 figures, 1 table, and 2 algorithms. Submitted to the International Geoscience and Remote Sensing Symposium (2021)

Compressive spectral imaging (CSI) has emerged as an alternative spectral image acquisition technology, which reduces the number of measurements at the cost of requiring a recovery process. In general, the reconstruction methods are based on hand-crafted priors used as regularizers in optimization algorithms or recent deep neural networks employed as an image generator to learn a non-linear mapping from the low-dimensional compressed measurements to the image space. However, these data-driven methods need many spectral images to obtain good performance. In this work, a deep recovery framework for CSI without training data is presented. The proposed method is based on the fact that the structure of some deep neural networks and an appropriated low-dimensional structure are sufficient to impose a structure of the underlying spectral image from CSI. We analyzed the low-dimension structure via the Tucker representation, modeled in the first net layer. The proposed scheme is obtained by minimizing the $\ell_2$-norm distance between the compressive measurements and the predicted measurements, and the desired recovered spectral image is formed just before the forward operator. Simulated and experimental results verify the effectiveness of the proposed method.

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing and communications applications, including denoising, spectrum sensing, and compression. Notice that estimating the covariance matrix from compressive samples leads to ill-posed minimizations with severe performance loss at high compression rates. In this regard, a regularization term is typically aggregated to the cost function to consider prior information about a particular property of the covariance matrix. Hence, this paper proposes an algorithm based on the projected gradient method to recover low-rank or Toeplitz approximations of the covariance matrix from compressive measurements. The algorithm divides the compressive measurements into data subsets projected onto different subspaces and accurately estimates the covariance matrix by solving a single optimization problem assuming that each data subset contains an approximation of the signal statistics. Furthermore, gradient filtering is included at every iteration of the proposed algorithm to minimize the estimation error. The error induced by the proposed splitting approach is analytically derived along with the convergence guarantees of the proposed method. The algorithm estimates the covariance matrix of hyperspectral images from synthetic and real compressive samples. Extensive simulations show that the proposed algorithm can effectively recover the covariance matrix of hyperspectral images from compressive measurements (8-15% approx). Moreover, simulations and theoretical results show that the filtering step reduces the recovery error up to twice the number of eigenvectors. Finally, an optical implementation is proposed, and real measurements are used to validate the theoretical findings., Comment: submitted to IEEE Transactions on Image Processing

In the compressive spectral imaging (CSI) framework, different architectures have been proposed to recover high-resolution spectral images from compressive measurements. Since CSI architectures compactly capture the relevant information of the spectral image, various methods that extract classification features from compressive samples have been recently proposed. However, these techniques require a feature extraction procedure that reorders measurements using the information embedded in the coded aperture patterns. In this paper, a method that fuses features directly from dual-resolution compressive measurements is proposed for spectral image classification. More precisely, the fusion method is formulated as an inverse problem that estimates high-spatial-resolution and low-dimensional feature bands from compressive measurements. To this end, the decimation matrices that describe the compressive measurements as degraded versions of the fused features are mathematically modeled using the information embedded in the coded aperture patterns. Furthermore, we include both a sparsity-promoting and a total-variation (TV) regularization terms to the fusion problem in order to consider the correlations between neighbor pixels, and therefore, improve the accuracy of pixel-based classifiers. To solve the fusion problem, we describe an algorithm based on the accelerated variant of the alternating direction method of multipliers (accelerated-ADMM). Additionally, a classification approach that includes the developed fusion method and a multilayer neural network is introduced. Finally, the proposed approach is evaluated on three remote sensing spectral images and a set of compressive measurements captured in the laboratory. Extensive simulations show that the proposed classification approach outperforms other approaches under various performance metrics., Comment: 24 pages, 12 figures and 3 tables

X-ray crystallography (XC) is an experimental technique used to determine three-dimensional crystalline structures. The acquired data in XC, called diffraction patterns, is the Fourier magnitudes of the unknown crystalline structure. To estimate the crystalline structure from its diffraction patterns, we propose to modify the traditional system by including an optical element called coded aperture which modulates the diffracted field to acquire coded diffraction patterns (CDP). For the proposed coded system, in contrast with the traditional, we derive exact reconstruction guarantees for the crystalline structure from CDP (up to a global shift phase). Additionally, exploiting the fact that the crystalline structure can be sparsely represented in the Fourier domain, we develop an algorithm to estimate the crystal structure from CDP. We show that this method requires 50% fewer measurements to estimate the crystal structure in comparison with its competitive alternatives. Specifically, the proposed method is able to reduce the exposition time of the crystal, implying that under the proposed setup, its structural integrity is less affected in comparison with the traditional. We discuss further implementation of imaging devices that exploits this theoretical coded system.

Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a time-shifted version of itself, for several different shifts. To estimate the pulse from the FROG trace, we propose an algorithm that minimizes a smoothed non-convex least-squares objective function. The method consists of two steps. First, we approximate the pulse by an iterative spectral algorithm. Then, the attained initialization is refined based upon a sequence of block stochastic gradient iterations. The algorithm is theoretically simple, numerically scalable, and easy-to-implement. Empirically, our approach outperforms the state-of-the-art when the FROG trace is incomplete, that is, when only few shifts are recorded. Simulations also suggest that the proposed algorithm exhibits similar computational cost compared to a state-of-the-art technique for both complete and incomplete data. In addition, we prove that in the vicinity of the true solution, the algorithm converges to a critical point. A Matlab implementation is publicly available at https://github.com/samuelpinilla/FROG., Comment: Simulations and comparisons are being added

Phase retrieval (PR) is an ill-conditioned inverse problem which can be found in various science and engineering applications. Assuming sparse priority over the signal of interest, recent algorithms have been developed to solve the phase retrieval problem. Some examples include SparseAltMinPhase (SAMP), Sparse Wirtinger flow (SWF) and Sparse Truncated Amplitude flow (SPARTA). However, the optimization cost functions of the mentioned algorithms are non-convex and non-smooth. In order to fix the non-smoothness of the cost function, the SPARTA method uses truncation thresholds to calculate a truncated step update direction. In practice, the truncation procedure requires calculating more parameters to obtain a desired performance in the phase recovery. Therefore, this paper proposes an algorithm called SPRSF (Sparse Phase retrieval via Smoothing Function) to solve the sparse PR problem by introducing a smoothing function. SPRSF is an iterative algorithm where the update step is obtained by a hard thresholding over a gradient descent direction. Theoretical analyses show that the smoothing function uniformly approximates the non-convex and non-smooth sparse PR optimization problem. Moreover, SPRSF does not require the truncation procedure used in SPARTA. Numerical tests demonstrate that SPRSF performs better than state-of-the-art methods, especially when there is no knowledge about the sparsity $k$. In particular, SPRSF attains a higher mean recovery rate in comparison with SPARTA, SAMP and SWF methods, when the sparsity varies for the real and complex cases. Further, in terms of the sampling complexity, the SPRSF method outperforms its competitive alternatives.