Petros T. Boufounos

Sorachi Kato, Ryoma Yataka, Pu Perry Wang et al.

Radar-based indoor 3D human pose estimation typically relied on fine-grained 3D keypoint labels, which are costly to obtain especially in complex indoor settings involving clutter, occlusions, or multiple people. In this paper, we propose \textbf{RAPTR} (RAdar Pose esTimation using tRansformer) under weak supervision, using only 3D BBox and 2D keypoint labels which are considerably easier and more scalable to collect. Our RAPTR is characterized by a two-stage pose decoder architecture with a pseudo-3D deformable attention to enhance (pose/joint) queries with multi-view radar features: a pose decoder estimates initial 3D poses with a 3D template loss designed to utilize the 3D BBox labels and mitigate depth ambiguities; and a joint decoder refines the initial poses with 2D keypoint labels and a 3D gravity loss. Evaluated on two indoor radar datasets, RAPTR outperforms existing methods, reducing joint position error by $34.3\%$ on HIBER and $76.9\%$ on MMVR. Our implementation is available at https://github.com/merlresearch/radar-pose-transformer.

Ryoma Yataka, Adriano Cardace, Pu Perry Wang et al.

Indoor radar perception has seen rising interest due to affordable costs driven by emerging automotive imaging radar developments and the benefits of reduced privacy concerns and reliability under hazardous conditions (e.g., fire and smoke). However, existing radar perception pipelines fail to account for distinctive characteristics of the multi-view radar setting. In this paper, we propose Radar dEtection TRansformer (RETR), an extension of the popular DETR architecture, tailored for multi-view radar perception. RETR inherits the advantages of DETR, eliminating the need for hand-crafted components for object detection and segmentation in the image plane. More importantly, RETR incorporates carefully designed modifications such as 1) depth-prioritized feature similarity via a tunable positional encoding (TPE); 2) a tri-plane loss from both radar and camera coordinates; and 3) a learnable radar-to-camera transformation via reparameterization, to account for the unique multi-view radar setting. Evaluated on two indoor radar perception datasets, our approach outperforms existing state-of-the-art methods by a margin of 15.38+ AP for object detection and 11.91+ IoU for instance segmentation, respectively. Our implementation is available at https://github.com/merlresearch/radar-detection-transformer.

Ryoma Yataka, Pu Perry Wang, Petros Boufounos et al.

Conventional radar feature extraction faces limitations due to low spatial resolution, noise, multipath reflection, the presence of ghost targets, and motion blur. Such limitations can be exacerbated by nonlinear object motion, particularly from an ego-centric viewpoint. It becomes evident that to address these challenges, the key lies in exploiting temporal feature relation over an extended horizon and enforcing spatial motion consistency for effective association. To this end, this paper proposes SIRA (Scalable Inter-frame Relation and Association) with two designs. First, inspired by Swin Transformer, we introduce extended temporal relation, generalizing the existing temporal relation layer from two consecutive frames to multiple inter-frames with temporally regrouped window attention for scalability. Second, we propose motion consistency track with the concept of a pseudo-tracklet generated from observational data for better trajectory prediction and subsequent object association. Our approach achieves 58.11 mAP@0.5 for oriented object detection and 47.79 MOTA for multiple object tracking on the Radiate dataset, surpassing previous state-of-the-art by a margin of +4.11 mAP@0.5 and +9.94 MOTA, respectively.

M. Mahbubur Rahman, Ryoma Yataka, Sorachi Kato et al.

Compared with an extensive list of automotive radar datasets that support autonomous driving, indoor radar datasets are scarce at a smaller scale in the format of low-resolution radar point clouds and usually under an open-space single-room setting. In this paper, we scale up indoor radar data collection using multi-view high-resolution radar heatmap in a multi-day, multi-room, and multi-subject setting, with an emphasis on the diversity of environment and subjects. Referred to as the millimeter-wave multi-view radar (MMVR) dataset, it consists of $345$K multi-view radar frames collected from $25$ human subjects over $6$ different rooms, $446$K annotated bounding boxes/segmentation instances, and $7.59$ million annotated keypoints to support three major perception tasks of object detection, pose estimation, and instance segmentation, respectively. For each task, we report performance benchmarks under two protocols: a single subject in an open space and multiple subjects in several cluttered rooms with two data splits: random split and cross-environment split over $395$ 1-min data segments. We anticipate that MMVR facilitates indoor radar perception development for indoor vehicle (robot/humanoid) navigation, building energy management, and elderly care for better efficiency, user experience, and safety. The MMVR dataset is available at https://doi.org/10.5281/zenodo.12611978.

Yanting Ma, Petros T. Boufounos, Hassan Mansour et al.

In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured subject to unknown permutations. In this paper we take a fresh look at this problem through the lens of optimal transport (OT). In particular, we recognize that in most practical applications the unknown permutations are not arbitrary but some are more likely to occur than others. We exploit this by introducing a regularization function that promotes the more likely permutations in the solution. We show that, even though the general problem is not convex, an appropriate relaxation of the resulting regularized problem allows us to exploit the well-developed machinery of OT and develop a tractable algorithm.

Ajinkya Kadu, Hassan Mansour, Petros T. Boufounos

Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects that commonly occurs in ground-penetrating radar, exploration geophysics, terahertz imaging, ultrasound, and electron microscopy. Unlike conventional transmission tomography, the reflection regime is severely ill-posed since the measured wavefields contain far less spatial frequency information of the target object. We propose a constrained incremental frequency inversion framework that requires no side information from a background model of the object. Our framework solves a sequence of regularized least-squares subproblems that ensure consistency with the measured scattered wavefield while imposing total-variation and non-negativity constraints. We propose a proximal Quasi-Newton method to solve the resulting subproblem and devise an automatic parameter selection routine to determine the constraint of each subproblem. We validate the performance of our approach on synthetic low-resolution phantoms and with a mismatched forward model test on a high-resolution phantom.

Hassan Mansour, Dehong Liu, Ulugbek S. Kamilov et al.

A common problem that arises in radar imaging systems, especially those mounted on mobile platforms, is antenna position ambiguity. Approaches to resolve this ambiguity and correct position errors are generally known as radar autofocus. Common techniques that attempt to resolve the antenna ambiguity generally assume an unknown gain and phase error afflicting the radar measurements. However, ensuring identifiability and tractability of the unknown error imposes strict restrictions on the allowable antenna perturbations. Furthermore, these techniques are often not applicable in near-field imaging, where mapping the position ambiguity to phase errors breaks down. In this paper, we propose an alternate formulation where the position error of each antenna is mapped to a spatial shift operator in the image-domain. Thus, the radar autofocus problem becomes a multichannel blind deconvolution problem, in which the radar measurements correspond to observations of a static radar image that is convolved with the spatial shift kernel associated with each antenna. To solve the reformulated problem, we also develop a block coordinate descent framework that leverages the sparsity and piece-wise smoothness of the radar scene, as well as the one-sparse property of the two dimensional shift kernels. We evaluate the performance of our approach using both simulated and experimental radar measurements, and demonstrate its superior performance compared to state-of-the-art methods.

Yanting Ma, Hassan Mansour, Dehong Liu et al.

The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship, there is an increased interest in considering nonlinear formulations that can account for multiple light scattering. In this paper, we propose an image reconstruction method, called CISOR, for nonlinear diffractive imaging, based on a nonconvex optimization formulation with total variation (TV) regularization. The nonconvex solver used in CISOR is our new variant of fast iterative shrinkage/thresholding algorithm (FISTA). We provide fast and memory-efficient implementation of the new FISTA variant and prove that it reliably converges for our nonconvex optimization problem. In addition, we systematically compare our method with other state-of-the-art methods on simulated as well as experimentally measured data in both 2D and 3D settings.

Kevin Degraux, Ulugbek S. Kamilov, Petros T. Boufounos et al.

Computational imaging methods that can exploit multiple modalities have the potential to enhance the capabilities of traditional sensing systems. In this paper, we propose a new method that reconstructs multimodal images from their linear measurements by exploiting redundancies across different modalities. Our method combines a convolutional group-sparse representation of images with total variation (TV) regularization for high-quality multimodal imaging. We develop an online algorithm that enables the unsupervised learning of convolutional dictionaries on large-scale datasets that are typical in such applications. We illustrate the benefit of our approach in the context of joint intensity-depth imaging.

Hsiou-Yuan Liu, Dehong Liu, Hassan Mansour et al.

Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with Accelerated Gradient Descent on Lippmann-Schwinger Equation (SEAGLE)-for robust imaging under multiple scattering based on a combination of a new nonlinear forward model and a total variation (TV) regularizer. The proposed forward model can account for multiple scattering, which makes it advantageous in applications where linear models are inaccurate. Specifically, it corresponds to a series expansion of the scattered wave with an accelerated-gradient method. This expansion guarantees the convergence even for strongly scattering objects. One of our key insights is that it is possible to obtain an explicit formula for computing the gradient of our nonlinear forward model with respect to the unknown object, thus enabling fast image reconstruction with the state-of-the-art fast iterative shrinkage/thresholding algorithm (FISTA). The proposed method is validated on both simulated and experimentally measured data.

Hsiou-Yuan Liu, Ulugbek S. Kamilov, Dehong Liu et al.

We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon, which makes the method preferable in applications where linear measurement models are inaccurate. We construct the measurement model by expanding the scattered wave-field with an accelerated-gradient method, which is guaranteed to converge and is suitable for large-scale problems. We provide explicit formulas for computing the gradient of our measurement model with respect to the unknown image, which enables image formation with a sparsity- driven numerical optimization algorithm. We validate the method both analytically and with numerical simulations.

Ulugbek S. Kamilov, Petros T. Boufounos

Spatial resolution of depth sensors is often significantly lower compared to that of conventional optical cameras. Recent work has explored the idea of improving the resolution of depth using higher resolution intensity as a side information. In this paper, we demonstrate that further incorporating temporal information in videos can significantly improve the results. In particular, we propose a novel approach that improves depth resolution, exploiting the space-time redundancy in the depth and intensity using motion-adaptive low-rank regularization. Experiments confirm that the proposed approach substantially improves the quality of the estimated high-resolution depth. Our approach can be a first component in systems using vision techniques that rely on high resolution depth information.

Petros T Boufounos, Shantanu Rane, Hassan Mansour

Approaches to signal representation and coding theory have traditionally focused on how to best represent signals using parsimonious representations that incur the lowest possible distortion. Classical examples include linear and non-linear approximations, sparse representations, and rate-distortion theory. Very often, however, the goal of processing is to extract specific information from the signal, and the distortion should be measured on the extracted information. The corresponding representation should, therefore, represent that information as parsimoniously as possible, without necessarily accurately representing the signal itself. In this paper, we examine the problem of encoding signals such that sufficient information is preserved about their pairwise distances and their inner products. For that goal, we consider randomized embeddings as an encoding mechanism and provide a framework to analyze their performance. We also demonstrate that it is possible to design the embedding such that it represents different ranges of distances with different precision. These embeddings also allow the computation of kernel inner products with control on their inner product-preserving properties. Our results provide a broad framework to design and analyze embeddins, and generalize existing results in this area, such as random Fourier kernels and universal embeddings.

Sohail Bahmani, Petros T. Boufounos, Bhiksha Raj

Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic exercise. Furthermore, the estimate that these methods produce might not belong to the desired sparsity model, albeit accurately approximating the true parameter. Therefore, greedy-type algorithms could often be more desirable in estimating structured-sparse parameters. So far, these greedy methods have mostly focused on linear statistical models. In this paper we study the projected gradient descent with non-convex structured-sparse parameter model as the constraint set. Should the cost function have a Stable Model-Restricted Hessian the algorithm produces an approximation for the desired minimizer. As an example we elaborate on application of the main results to estimation in Generalized Linear Model.

Sohail Bahmani, Bhiksha Raj, Petros Boufounos

Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained optimization from theoretical, algorithmic, and application aspects in the context of sparse estimation in linear models where the fidelity of the estimate is measured by the squared error. In contrast, relatively less effort has been made in the study of sparsity-constrained optimization in cases where nonlinear models are involved or the cost function is not quadratic. In this paper we propose a greedy algorithm, Gradient Support Pursuit (GraSP), to approximate sparse minima of cost functions of arbitrary form. Should a cost function have a Stable Restricted Hessian (SRH) or a Stable Restricted Linearization (SRL), both of which are introduced in this paper, our algorithm is guaranteed to produce a sparse vector within a bounded distance from the true sparse optimum. Our approach generalizes known results for quadratic cost functions that arise in sparse linear regression and Compressive Sensing. We also evaluate the performance of GraSP through numerical simulations on synthetic data, where the algorithm is employed for sparse logistic regression with and without $\ell_2$-regularization.

Mark A. Davenport, Jason N. Laska, Petros T. Boufounos et al.

The recently introduced theory of compressive sensing (CS) enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be significantly smaller than the ambient dimension of the signal and yet preserve the significant signal information. Interestingly, it can be shown that random measurement schemes provide a near-optimal encoding in terms of the required number of measurements. In this report, we explore another relatively unexplored, though often alluded to, advantage of using random matrices to acquire CS measurements. Specifically, we show that random matrices are democractic, meaning that each measurement carries roughly the same amount of signal information. We demonstrate that by slightly increasing the number of measurements, the system is robust to the loss of a small number of arbitrary measurements. In addition, we draw connections to oversampling and demonstrate stability from the loss of significantly more measurements.