arXiv subjects

Ajit Rajwade

Publications and source records attributed to Ajit Rajwade.

At least 19 recordsLinked to original sources

arXiv2026

Correction of Pooling Matrix Mis-specifications in Compressed Sensing Based Group Testing

Compressed sensing, which involves the reconstruction of sparse signals from an under-determined linear system, has been recently used to solve problems in group testing. In a public health context, group testing aims to determine the health status values of p subjects from n<<p pooled tests, where a pool is defined as a mixture of small, equal-volume portions of the samples of a subset of subjects. This approach saves on the number of tests administered in pandemics or other resource-constrained scenarios. In practical group testing in time-constrained situations, a technician can inadvertently make a small number of errors during pool preparation, which leads to errors in the pooling matrix, which we term `model mismatch errors' (MMEs). This poses difficulties while determining health status values of the participating subjects from the results on n<<p pooled tests. In this paper, we present an algorithm to correct the MMEs in the pooled tests directly from the pooled results and the available (inaccurate) pooling matrix. Our approach then reconstructs the signal vector from the corrected pooling matrix, in order to determine the health status of the subjects. We further provide theoretical guarantees for the correction of the MMEs and the reconstruction error from the corrected pooling matrix. We also provide several supporting numerical results.

stat.AP↗

arXiv2025

Verifiable Deep Quantitative Group Testing

We present a neural network-based framework for solving the quantitative group testing (QGT) problem that achieves both high decoding accuracy and structural verifiability. In QGT, the objective is to identify a small subset of defective items among $N$ candidates using only $M \ll N$ pooled tests, each reporting the number of defectives in the tested subset. We train a multi-layer perceptron to map noisy measurement vectors to binary defect indicators, achieving accurate and robust recovery even under sparse, bounded perturbations. Beyond accuracy, we show that the trained network implicitly learns the underlying pooling structure that links items to tests, allowing this structure to be recovered directly from the network's Jacobian. This indicates that the model does not merely memorize training patterns but internalizes the true combinatorial relationships governing QGT. Our findings reveal that standard feedforward architectures can learn verifiable inverse mappings in structured combinatorial recovery problems.

eess.SP↗

arXiv2025

Two-Dimensional Tomographic Reconstruction From Projections With Unknown Angles and Unknown Spatial Shifts

In parallel beam computed tomography (CT), an object is reconstructed from a series of projections taken at different angles. However, in some industrial and biomedical imaging applications, the projection geometry is unknown, completely or partially. In this paper, we present a technique for two-dimensional (2D) tomography in which both viewing angles and spatial shifts associated with the projections are unknown. There exists literature on 2D unknown view tomography (UVT), but most existing 2D UVT algorithms assume that the projections are centered; that is, there are no spatial shifts in the projections. To tackle these geometric ambiguities, we first modify an existing graph Laplacian-based algorithm for 2D UVT to incorporate spatial shifts, and then use it as the initialization for the proposed three-way alternating minimization algorithm that jointly estimates the 2D structure, its projection angles, and the corresponding shifts. We evaluate our method on noisy projections of ribosome images and demonstrate that it achieves superior reconstruction compared to the baseline that neglects shifts.

eess.IV↗

arXiv2025

3-Dimensional CryoEM Pose Estimation and Shift Correction Pipeline

Accurate pose estimation and shift correction are key challenges in cryo-EM due to the very low SNR, which directly impacts the fidelity of 3D reconstructions. We present an approach for pose estimation in cryo-EM that leverages multi-dimensional scaling (MDS) techniques in a robust manner to estimate the 3D rotation matrix of each particle from pairs of dihedral angles. We express the rotation matrix in the form of an axis of rotation and a unit vector in the plane perpendicular to the axis. The technique leverages the concept of common lines in 3D reconstruction from projections. However, common line estimation is ridden with large errors due to the very low SNR of cryo-EM projection images. To address this challenge, we introduce two complementary components: (i) a robust joint optimization framework for pose estimation based on an $\ell_1$-norm objective or a similar robust norm, which simultaneously estimates rotation axes and in-plane vectors while exactly enforcing unit norm and orthogonality constraints via projected coordinate descent; and (ii) an iterative shift correction algorithm that estimates consistent in-plane translations through a global least-squares formulation. While prior approaches have leveraged such embeddings and common-line geometry for orientation recovery, existing formulations typically rely on $\ell_2$-based objectives that are sensitive to noise, and enforce geometric constraints only approximately. These choices, combined with a sequential pipeline structure, can lead to compounding errors and suboptimal reconstructions in low-SNR regimes. Our pipeline consistently outperforms prior methods in both Euler angle accuracy and reconstruction fidelity, as measured by the Fourier Shell Correlation (FSC).

cs.CV↗

arXiv2025

Dictionary-Based Reconstruction of Spatio-Temporal 3D Magnetic Field Images from Quantum Diamond Microscope

Three-dimensional magnetic imaging with high spatio-temporal resolution is critical for probing current paths in various systems, from biosensing to microelectronics. Conventional 2D Fourier-based current source localization methods are ill-posed in multilayer or dynamic systems due to signal overlap and noise. In this work, we demonstrate an innovative nitrogen-vacancy (NV) center-based wide-field magnetic microscopy technique for dynamic three-dimensional imaging and localization of current sources. Using custom-fabricated multilayer micro-coil platform to emulate localized, time-varying currents similar to neuronal activity, we acquire magnetic field maps with micrometre-scale spatial and millisecond-scale temporal resolution using per-pixel lock-in-based detection. Source localization and image reconstruction are achieved using a Least Absolute Shrinkage and Selection Operator (LASSO)-based reconstruction framework that incorporates experimentally measured basis maps as spatial priors. Our method enables robust identification of active current sources across space and time, and significantly advances the accuracy of dynamic 3D current imaging and NV-based magnetometry for complex systems.

physics.ins-det↗

arXiv2025

Fast Debiasing of the LASSO Estimator

In high-dimensional sparse regression, the \textsc{Lasso} estimator offers excellent theoretical guarantees but is well-known to produce biased estimates. To address this, \cite{Javanmard2014} introduced a method to ``debias" the \textsc{Lasso} estimates for a random sub-Gaussian sensing matrix $\boldsymbol{A}$. Their approach relies on computing an ``approximate inverse" $\boldsymbol{M}$ of the matrix $\boldsymbol{A}^\top \boldsymbol{A}/n$ by solving a convex optimization problem. This matrix $\boldsymbol{M}$ plays a critical role in mitigating bias and allowing for construction of confidence intervals using the debiased \textsc{Lasso} estimates. However the computation of $\boldsymbol{M}$ is expensive in practice as it requires iterative optimization. In the presented work, we re-parameterize the optimization problem to compute a ``debiasing matrix" $\boldsymbol{W} := \boldsymbol{AM}^{\top}$ directly, rather than the approximate inverse $\boldsymbol{M}$. This reformulation retains the theoretical guarantees of the debiased \textsc{Lasso} estimates, as they depend on the \emph{product} $\boldsymbol{AM}^{\top}$ rather than on $\boldsymbol{M}$ alone. Notably, we provide a simple, computationally efficient, closed-form solution for $\boldsymbol{W}$ under similar conditions for the sensing matrix $\boldsymbol{A}$ used in the original debiasing formulation, with an additional condition that the elements of every row of $\boldsymbol{A}$ have uncorrelated entries. Also, the optimization problem based on $\boldsymbol{W}$ guarantees a unique optimal solution, unlike the original formulation based on $\boldsymbol{M}$. We verify our main result with numerical simulations.

stat.ML↗

arXiv2025

Two-Dimensional Unknown View Tomography from Unknown Angle Distributions

This study presents a technique for 2D tomography under unknown viewing angles when the distribution of the viewing angles is also unknown. Unknown view tomography (UVT) is a problem encountered in cryo-electron microscopy and in the geometric calibration of CT systems. There exists a moderate-sized literature on the 2D UVT problem, but most existing 2D UVT algorithms assume knowledge of the angle distribution which is not available usually. Our proposed methodology formulates the problem as an optimization task based on cross-validation error, to estimate the angle distribution jointly with the underlying 2D structure in an alternating fashion. We explore the algorithm's capabilities for the case of two probability distribution models: a semi-parametric mixture of von Mises densities and a probability mass function model. We evaluate our algorithm's performance under noisy projections using a PCA-based denoising technique and Graph Laplacian Tomography (GLT) driven by order statistics of the estimated distribution, to ensure near-perfect ordering, and compare our algorithm to intuitive baselines.

cs.CV↗

arXiv2024

Robust Non-adaptive Group Testing under Errors in Group Membership Specifications

Given $p$ samples, each of which may or may not be defective, group testing (GT) aims to determine their defect status by performing tests on $n < p$ `groups', where a group is formed by mixing a subset of the $p$ samples. Assuming that the number of defective samples is very small compared to $p$, GT algorithms have provided excellent recovery of the status of all $p$ samples with even a small number of groups. Most existing methods, however, assume that the group memberships are accurately specified. This assumption may not always be true in all applications, due to various resource constraints. Such errors could occur, eg, when a technician, preparing the groups in a laboratory, unknowingly mixes together an incorrect subset of samples as compared to what was specified. We develop a new GT method, the Debiased Robust Lasso Test Method (DRLT), that handles such group membership specification errors. The proposed DRLT method is based on an approach to debias, or reduce the inherent bias in, estimates produced by Lasso, a popular and effective sparse regression technique. We also provide theoretical upper bounds on the reconstruction error produced by our estimator. Our approach is then combined with two carefully designed hypothesis tests respectively for (i) the identification of defective samples in the presence of errors in group membership specifications, and (ii) the identification of groups with erroneous membership specifications. The DRLT approach extends the literature on bias mitigation of statistical estimators such as the LASSO, to handle the important case when some of the measurements contain outliers, due to factors such as group membership specification errors. We present numerical results which show that our approach outperforms several baselines and robust regression techniques for identification of defective samples as well as erroneously specified groups.

stat.ML↗

arXiv2024

Compressive Recovery of Signals Defined on Perturbed Graphs

Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios, the graph may not be accurately known, and there may exist a few edge additions or deletions relative to a ground truth graph. Such perturbations, even if small in number, significantly affect the Graph Fourier Transform (GFT). This impedes recovery of signals which may have sparse representations in the GFT bases of the ground truth graph. We present an algorithm which simultaneously recovers the signal from the compressive measurements and also corrects the graph perturbations. We analyze some important theoretical properties of the algorithm. Our approach to correction for graph perturbations is based on model selection techniques such as cross-validation in compressed sensing. We validate our algorithm on signals which have a sparse representation in the GFT bases of many commonly used graphs in the network science literature. An application to compressive image reconstruction is also presented, where graph perturbations are modeled as undesirable graph edges linking pixels with significant intensity difference. In all experiments, our algorithm clearly outperforms baseline techniques which either ignore the perturbations or use first order approximations to the perturbations in the GFT bases.

eess.SP↗

arXiv2023

Group Testing for Accurate and Efficient Range-Based Near Neighbor Search for Plagiarism Detection

This work presents an adaptive group testing framework for the range-based high dimensional near neighbor search problem. Our method efficiently marks each item in a database as neighbor or non-neighbor of a query point, based on a cosine distance threshold without exhaustive search. Like other methods for large scale retrieval, our approach exploits the assumption that most of the items in the database are unrelated to the query. However, it does not assume a large difference between the cosine similarity of the query vector with the least related neighbor and that with the least unrelated non-neighbor. Following a multi-stage adaptive group testing algorithm based on binary splitting, we divide the set of items to be searched into half at each step, and perform dot product tests on smaller and smaller subsets, many of which we are able to prune away. We show that, using softmax-based features, our method achieves a more than ten-fold speed-up over exhaustive search with no loss of accuracy, on a variety of large datasets. Based on empirically verified models for the distribution of cosine distances, we present a theoretical analysis of the expected number of distance computations per query and the probability that a pool will be pruned. Our method has the following features: (i) It implicitly exploits useful distributional properties of cosine distances unlike other methods; (ii) All required data structures are created purely offline; (iii) It does not impose any strong assumptions on the number of true near neighbors; (iv) It is adaptable to streaming settings where new vectors are dynamically added to the database; and (v) It does not require any parameter tuning. The high recall of our technique makes it particularly suited to plagiarism detection scenarios where it is important to report every database item that is sufficiently similar item to the query.

cs.DS↗

arXiv2023

Unlabelled Sensing with Priors: Algorithm and Bounds

In this study, we consider a variant of unlabelled sensing where the measurements are sparsely permuted, and additionally, a few correspondences are known. We present an estimator to solve for the unknown vector. We derive a theoretical upper bound on the $\ell_2$ reconstruction error of the unknown vector. Through numerical experiments, we demonstrate that the additional known correspondences result in a significant improvement in the reconstruction error. Additionally, we compare our estimator with the classical robust regression estimator and we find that our method outperforms it on the normalized reconstruction error metric by up to $20\%$ in the high permutation regimes $(>30\%)$. Lastly, we showcase the practical utility of our framework on a non-rigid motion estimation problem. We show that using a few manually annotated points along point pairs with the key-point (SIFT-based) descriptor pairs with unknown or incorrectly known correspondences can improve motion estimation.

eess.SP↗

arXiv2023

Performance Bounds for LASSO under Multiplicative Noise: Applications to Pooled RT-PCR Testing

Group testing is a technique which avoids individually testing $n$ samples for a rare disease and instead tests $n < p$ pools, where a pool consists of a mixture of small, equal portions of a subset of the $p$ samples. Group testing saves testing time and resources in many applications, including RT-PCR, with guarantees for the recovery of the status of the $p$ samples from results on $n$ pools. The noise in quantitative RT- PCR is inherently known to follow a multiplicative data-dependent model. In recent literature, the corresponding linear systems for inferring the health status of $p$ samples from results on $n$ pools have been solved using the Lasso estimator and its variants, which have been typically used in additive Gaussian noise settings. There is no existing literature which establishes performance bounds for Lasso for the multiplicative noise model associated with RT-PCR. After noting that a recent general technique, Hunt et al., works for Poisson inverse problems, we adapt it to handle sparse signal reconstruction from compressive measurements with multiplicative noise: we present high probability performance bounds and data-dependent weights for the Lasso and its weighted version. We also show numerical results on simulated pooled RT-PCR data to empirically validate our bounds.

math.ST↗

arXiv2023

Group Testing with Side Information via Generalized Approximate Message Passing

Group testing can help maintain a widespread testing program using fewer resources amid a pandemic. In a group testing setup, we are given n samples, one per individual. Each individual is either infected or uninfected. These samples are arranged into m < n pooled samples, where each pool is obtained by mixing a subset of the n individual samples. Infected individuals are then identified using a group testing algorithm. In this paper, we incorporate side information (SI) collected from contact tracing (CT) into nonadaptive/single-stage group testing algorithms. We generate different types of possible CT SI data by incorporating different possible characteristics of the spread of disease. These data are fed into a group testing framework based on generalized approximate message passing (GAMP). Numerical results show that our GAMP-based algorithms provide improved accuracy.

eess.SP↗

arXiv2023

Efficient Neural Network based Classification and Outlier Detection for Image Moderation using Compressed Sensing and Group Testing

Popular social media platforms employ neural network based image moderation engines to classify images uploaded on them as having potentially objectionable content. Such moderation engines must answer a large number of queries with heavy computational cost, even though the actual number of images with objectionable content is usually a tiny fraction. Inspired by recent work on Neural Group Testing, we propose an approach which exploits this fact to reduce the overall computational cost of such engines using the technique of Compressed Sensing (CS). We present the quantitative matrix-pooled neural network (QMPNN), which takes as input $n$ images, and a $m \times n$ binary pooling matrix with $m < n$, whose rows indicate $m$ pools of images i.e. selections of $r$ images out of $n$. The QMPNN efficiently outputs the product of this matrix with the unknown sparse binary vector indicating whether each image is objectionable or not, i.e. it outputs the number of objectionable images in each pool. For suitable matrices, this is decoded using CS decoding algorithms to predict which images were objectionable. The computational cost of running the QMPNN and the CS algorithms is significantly lower than the cost of using a neural network with the same number of parameters separately on each image to classify the images, which we demonstrate via extensive experiments. Our technique is inherently resilient to moderate levels of errors in the prediction from the QMPNN. Furthermore, we present pooled deep outlier detection, which brings CS and group testing techniques to deep outlier detection, to provide for the case when the objectionable images do not belong to a set of pre-defined classes. This technique enables efficient automated moderation of off-topic images shared on topical forums dedicated to sharing images of a certain single class, many of which are currently human-moderated.

cs.CV↗

arXiv2023

Estimating Joint Probability Distribution With Low-Rank Tensor Decomposition, Radon Transforms and Dictionaries

In this paper, we describe a method for estimating the joint probability density from data samples by assuming that the underlying distribution can be decomposed as a mixture of product densities with few mixture components. Prior works have used such a decomposition to estimate the joint density from lower-dimensional marginals, which can be estimated more reliably with the same number of samples. We combine two key ideas: dictionaries to represent 1-D densities, and random projections to estimate the joint distribution from 1-D marginals, explored separately in prior work. Our algorithm benefits from improved sample complexity over the previous dictionary-based approach by using 1-D marginals for reconstruction. We evaluate the performance of our method on estimating synthetic probability densities and compare it with the previous dictionary-based approach and Gaussian Mixture Models (GMMs). Our algorithm outperforms these other approaches in all the experimental settings.

stat.ML↗

arXiv2023

Signal Reconstruction from Samples at Unknown Locations with Application to 2D Unknown View Tomography

It is well known that a band-limited signal can be reconstructed from its uniformly spaced samples if the sampling rate is sufficiently high. More recently, it has been proved that one can reconstruct a 1D band-limited signal even if the exact sample locations are unknown, but given a uniform distribution of the sample locations and their ordering in 1D. In this work, we extend the analytical error bounds in such scenarios for quasi-bandlimited (QBL) signals, and for the case of arbitrary but known sampling distributions. We also prove that such reconstruction methods are resilient to a certain proportion of errors in the specification of the sample location ordering. We then express the problem of tomographic reconstruction of 2D images from 1D Radon projections under unknown angles (2D UVT) with known angle distribution, as a special case for reconstruction of QBL signals from samples at unknown locations with known distribution. Building upon our theoretical background, we present asymptotic bounds for 2D QBL image reconstruction from 1D Radon projections in the unknown angles setting, and present an extensive set of simulations to verify these bounds in varied parameter regimes. To the best of our knowledge, this is the first piece of work to perform such an analysis for 2D UVT and explicitly relate it to advances in sampling theory, even though the associated reconstruction algorithms have been known for a long time.

cs.CV↗

arXiv2022

GlobalFlowNet: Video Stabilization using Deep Distilled Global Motion Estimates

Videos shot by laymen using hand-held cameras contain undesirable shaky motion. Estimating the global motion between successive frames, in a manner not influenced by moving objects, is central to many video stabilization techniques, but poses significant challenges. A large body of work uses 2D affine transformations or homography for the global motion. However, in this work, we introduce a more general representation scheme, which adapts any existing optical flow network to ignore the moving objects and obtain a spatially smooth approximation of the global motion between video frames. We achieve this by a knowledge distillation approach, where we first introduce a low pass filter module into the optical flow network to constrain the predicted optical flow to be spatially smooth. This becomes our student network, named as \textsc{GlobalFlowNet}. Then, using the original optical flow network as the teacher network, we train the student network using a robust loss function. Given a trained \textsc{GlobalFlowNet}, we stabilize videos using a two stage process. In the first stage, we correct the instability in affine parameters using a quadratic programming approach constrained by a user-specified cropping limit to control loss of field of view. In the second stage, we stabilize the video further by smoothing global motion parameters, expressed using a small number of discrete cosine transform coefficients. In extensive experiments on a variety of different videos, our technique outperforms state of the art techniques in terms of subjective quality and different quantitative measures of video stability. The source code is publicly available at \href{https://github.com/GlobalFlowNet/GlobalFlowNet}{https://github.com/GlobalFlowNet/GlobalFlowNet}

cs.CV↗

arXiv2022

Joint Probability Estimation Using Tensor Decomposition and Dictionaries

In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be decomposed and approximated by a mixture of product densities/mass functions. The problem of estimating the joint probability density function (PDF) using semi-parametric techniques such as Gaussian Mixture Models (GMMs) is widely studied. However such techniques yield poor results when the underlying densities are mixtures of various other families of distributions such as Laplacian or generalized Gaussian, uniform, Cauchy, etc. Further, GMMs are not the best choice to estimate joint distributions which are hybrid in nature, i.e., some random variables are discrete while others are continuous. We present a novel approach for estimating the PDF using ideas from dictionary representations in signal processing coupled with low rank tensor decompositions. To the best our knowledge, this is the first work on estimating joint PDFs employing dictionaries alongside tensor decompositions. We create a dictionary of various families of distributions by inspecting the data, and use it to approximate each decomposed factor of the product in the mixture. Our approach can naturally handle hybrid $N$-dimensional distributions. We test our approach on a variety of synthetic and real datasets to demonstrate its effectiveness in terms of better classification rates and lower error rates, when compared to state of the art estimators.

cs.LG↗