arXiv subjects

Marco F. Duarte

Publications and source records attributed to Marco F. Duarte.

At least 19 recordsLinked to original sources

arXiv2026

HyperBench: Standardizing and Scaling Synthetic Evaluation for Hyperspectral Super-Resolution

Hyperspectral super-resolution (HSR) reconstructs a high-spatial-resolution hyperspectral image by fusing a low-resolution hyperspectral image (LR-HSI) with a high-resolution multispectral image (HR-MSI). In the absence of real-world paired data, HSR methods are evaluated almost exclusively on synthetic experiments derived from hyperspectral datasets through Wald's protocol. Despite the protocol's widespread adoption, its practical implementation varies markedly across research works, typically relying on a single (usually Gaussian) or very few point spread functions (PSFs), one or two spectral response functions (SRFs), and a couple of spatial downsampling factors. As a result, reported performance figures are difficult to compare across the literature, in addition to being often difficult to reproduce; furthermore, they may not generalize across realistic sensing conditions. We introduce HyperBench, a unified and extensible framework that standardizes synthetic experimentation for HSR. HyperBench supports diverse degradation configurations spanning ten PSFs, four SRFs derived from operational multispectral sensors, configurable spatial downsampling factors, and matched additive white Gaussian noise; its goal is to automate large-scale evaluation and structured logging. By decoupling model development from experimental design, the framework enables reproducible, apples-to-apples cross-method comparison with minimal friction. We use HyperBench to evaluate six recently proposed HSR methods across a 70-configuration sweep on four widely used hyperspectral scenes and observe that the inter-method PSNR spread widens from approximately 5 dB on the easiest PSF to over 13 dB on the hardest - a fragility that is structurally invisible to the prevailing single-configuration evaluation protocol. HyperBench code is available at https://github.com/ritikgshah/HyperBench .

eess.IV↗

arXiv2025

Affine Subspace Models and Clustering for Patch-Based Image Denoising

Image tile-based approaches are popular in many image processing applications such as denoising (e.g., non-local means). A key step in their use is grouping the images into clusters, which usually proceeds iteratively splitting the images into clusters and fitting a model for the images in each cluster. Linear subspaces have emerged as a suitable model for tile clusters; however, they are not well matched to images patches given that images are non-negative and thus not distributed around the origin in the tile vector space. We study the use of affine subspace models for the clusters to better match the geometric structure of the image tile vector space. We also present a simple denoising algorithm that relies on the affine subspace clustering model using least squares projection. We review several algorithmic approaches to solve the affine subspace clustering problem and show experimental results that highlight the performance improvements in clustering and denoising.

eess.IV↗

arXiv2025

SpectraLift: Physics-Guided Spectral-Inversion Network for Self-Supervised Hyperspectral Image Super-Resolution

High-spatial-resolution hyperspectral images (HSI) are essential for applications such as remote sensing and medical imaging, yet HSI sensors inherently trade spatial detail for spectral richness. Fusing high-spatial-resolution multispectral images (HR-MSI) with low-spatial-resolution hyperspectral images (LR-HSI) is a promising route to recover fine spatial structures without sacrificing spectral fidelity. Most state-of-the-art methods for HSI-MSI fusion demand point spread function (PSF) calibration or ground truth high resolution HSI (HR-HSI), both of which are impractical to obtain in real world settings. We present SpectraLift, a fully self-supervised framework that fuses LR-HSI and HR-MSI inputs using only the MSI's Spectral Response Function (SRF). SpectraLift trains a lightweight per-pixel multi-layer perceptron (MLP) network using ($i$)~a synthetic low-spatial-resolution multispectral image (LR-MSI) obtained by applying the SRF to the LR-HSI as input, ($ii$)~the LR-HSI as the output, and ($iii$)~an $\ell_1$ spectral reconstruction loss between the estimated and true LR-HSI as the optimization objective. At inference, SpectraLift uses the trained network to map the HR-MSI pixel-wise into a HR-HSI estimate. SpectraLift converges in minutes, is agnostic to spatial blur and resolution, and outperforms state-of-the-art methods on PSNR, SAM, SSIM, and RMSE benchmarks.

eess.IV↗

arXiv2020

Binary Sequence Set Design for Interferer Rejection in Multi-Branch Modulation

Wideband communication is often expected to deal with a very wide spectrum, which in many environments of interest includes strong interferers. Thus receivers for the wideband communication systems often need to mitigate interferers to reduce the distortion caused by the amplifier nonlinearity and noise. Recently, a new architecture for communication receivers known as random modulation mixes a signal with different pseudorandom sequences using multiple branches of channels before sampling. While random modulation is used in these receivers to acquire the signal at low sampling rates, the modulation sequences used lack the ability to suppress interferers due to their flat spectra. In previous work, we introduced the design of a single spectrally shaped binary sequence that mitigates interferers to replace the pseudorandom sequence in a channel. However, the designed sequences cannot provide the stable recovery achieved by pseudorandom sequence approaches. In this paper, we extend our previous sequence design to guarantee stable recovery by designing a set of sequences to be orthogonal to each other. We show that it is difficult to find the necessary number of sequences featuring mutual orthogonality and introduce oversampling to the sequence set design to improve the recovery performance. We propose an algorithm for multi-branch sequence design as a binary optimization problem, which is solved using a semidefinite program relaxation and randomized projection. While it is common to model narrowband interferers as a subspace spanned by a subset of elements from the Fourier basis, we show that the Slepian basis provides an alternative and more suitable compact representation for signals with components contained in narrow spectrum bands. Numerical experiments using the proposed sequence sets show their advantages against pseudorandom sequences and our previous work.

cs.IT↗

arXiv2020

Explainable Machine Learning for Scientific Insights and Discoveries

Machine learning methods have been remarkably successful for a wide range of application areas in the extraction of essential information from data. An exciting and relatively recent development is the uptake of machine learning in the natural sciences, where the major goal is to obtain novel scientific insights and discoveries from observational or simulated data. A prerequisite for obtaining a scientific outcome is domain knowledge, which is needed to gain explainability, but also to enhance scientific consistency. In this article we review explainable machine learning in view of applications in the natural sciences and discuss three core elements which we identified as relevant in this context: transparency, interpretability, and explainability. With respect to these core elements, we provide a survey of recent scientific works that incorporate machine learning and the way that explainable machine learning is used in combination with domain knowledge from the application areas.

cs.LG↗

arXiv2019

Autoencoder Based Sample Selection for Self-Taught Learning

Self-taught learning is a technique that uses a large number of unlabeled data as source samples to improve the task performance on target samples. Compared with other transfer learning techniques, self-taught learning can be applied to a broader set of scenarios due to the loose restrictions on the source data. However, knowledge transferred from source samples that are not sufficiently related to the target domain may negatively influence the target learner, which is referred to as negative transfer. In this paper, we propose a metric for the relevance between a source sample and the target samples. To be more specific, both source and target samples are reconstructed through a single-layer autoencoder with a linear relationship between source samples and reconstructed target samples being simultaneously enforced. An $\ell_{2,1}$-norm sparsity constraint is imposed on the transformation matrix to identify source samples relevant to the target domain. Source domain samples that are deemed relevant are assigned pseudo-labels reflecting their relevance to target domain samples, and are combined with target samples in order to provide an expanded training set for classifier training. Local data structures are also preserved during source sample selection through spectral graph analysis. Promising results in extensive experiments show the advantages of the proposed approach.

cs.LG↗

arXiv2019

Few-Shot Learning-Based Human Activity Recognition

Few-shot learning is a technique to learn a model with a very small amount of labeled training data by transferring knowledge from relevant tasks. In this paper, we propose a few-shot learning method for wearable sensor based human activity recognition, a technique that seeks high-level human activity knowledge from low-level sensor inputs. Due to the high costs to obtain human generated activity data and the ubiquitous similarities between activity modes, it can be more efficient to borrow information from existing activity recognition models than to collect more data to train a new model from scratch when only a few data are available for model training. The proposed few-shot human activity recognition method leverages a deep learning model for feature extraction and classification while knowledge transfer is performed in the manner of model parameter transfer. In order to alleviate negative transfer, we propose a metric to measure cross-domain class-wise relevance so that knowledge of higher relevance is assigned larger weights during knowledge transfer. Promising results in extensive experiments show the advantages of the proposed approach.

cs.LG↗

arXiv2018

Design of Spectrally Shaped Binary Sequences via Randomized Convex Relaxation

Wideband communication receivers often deal with the problems of detecting weak signals from distant sources received together with strong nearby interferers. When the techniques of random modulation are used in communication system receivers, one can design a spectrally shaped sequence that mitigates interferer bands while preserving message bands. Common implementation constraints require sequence quantization, which turns the design problem formulation to an integer optimization problem solved using a semidefinite program on a matrix that is restricted to have rank one. Common approximation schemes for this problem are not amenable due to the distortion to the spectrum caused by the required quantization. We propose a method that leverages a randomized projection and quantization of the solution of a semidefinite program, an approach that has been previously used for related integer programs. We provide a theoretical and numerical analysis on the feasibility and quality of the approximation provided by the proposed approach. Furthermore, numerical simulations show that our proposed approach returns the same sequence as an exhaustive search (when feasible), showcasing its accuracy and efficiency. Furthermore, our proposed method succeeds in finding suitable spectrally shaped sequences for cases where exhaustive search is not feasible, achieving better performance than existing alternatives.

cs.IT↗

arXiv2018

Graph Autoencoder-Based Unsupervised Feature Selection with Broad and Local Data Structure Preservation

Feature selection is a dimensionality reduction technique that selects a subset of representative features from high dimensional data by eliminating irrelevant and redundant features. Recently, feature selection combined with sparse learning has attracted significant attention due to its outstanding performance compared with traditional feature selection methods that ignores correlation between features. These works first map data onto a low-dimensional subspace and then select features by posing a sparsity constraint on the transformation matrix. However, they are restricted by design to linear data transformation, a potential drawback given that the underlying correlation structures of data are often non-linear. To leverage a more sophisticated embedding, we propose an autoencoder-based unsupervised feature selection approach that leverages a single-layer autoencoder for a joint framework of feature selection and manifold learning. More specifically, we enforce column sparsity on the weight matrix connecting the input layer and the hidden layer, as in previous work. Additionally, we include spectral graph analysis on the projected data into the learning process to achieve local data geometry preservation from the original data space to the low-dimensional feature space. Extensive experiments are conducted on image, audio, text, and biological data. The promising experimental results validate the superiority of the proposed method.

cs.CV↗

arXiv2017

Out-of-Sample Extension for Dimensionality Reduction of Noisy Time Series

This paper proposes an out-of-sample extension framework for a global manifold learning algorithm (Isomap) that uses temporal information in out-of-sample points in order to make the embedding more robust to noise and artifacts. Given a set of noise-free training data and its embedding, the proposed framework extends the embedding for a noisy time series. This is achieved by adding a spatio-temporal compactness term to the optimization objective of the embedding. To the best of our knowledge, this is the first method for out-of-sample extension of manifold embeddings that leverages timing information available for the extension set. Experimental results demonstrate that our out-of-sample extension algorithm renders a more robust and accurate embedding of sequentially ordered image data in the presence of various noise and artifacts when compared to other timing-aware embeddings. Additionally, we show that an out-of-sample extension framework based on the proposed algorithm outperforms the state of the art in eye-gaze estimation.

stat.ML↗

arXiv2017

Performance of Compressive Parameter Estimation via K-Median Clustering

Compressive sensing (CS) has attracted significant attention in parameter estimation tasks, where parametric dictionaries (PDs) collect signal observations for a sampling of the parameter space and yield sparse representations for signals of interest when the sampling is dense. While this sampling also leads to high dictionary coherence, one can leverage structured sparsity models to prevent highly coherent dictionary elements from appearing simultaneously in the recovered signal. However, the resulting approaches depend heavily on the careful setting of the maximum allowable coherence; furthermore, their guarantees are not concerned with general parameter estimation performance. We propose the use of earth mover's distance (EMD), as applied to a pair of true and estimated PD coefficient vectors, to measure the parameter estimation error. We formally analyze the connection between the EMD and the parameter estimation error and show that the EMD provides a better-suited metric for parameter estimation performance than the Euclidean distance. Additionally, we analyze the previously described relationship between K-median clustering and EMD-optimal sparse approximation and leverage it to develop improved PD-based parameter estimation algorithms. Finally, our numerical experiments verify our theoretical results and show that the proposed compressive parameter estimation algorithms have improved performance over existing approaches.

cs.IT↗

arXiv2017

Semi-Supervised Endmember Identification In Nonlinear Spectral Mixtures Via Semantic Representation

This paper proposes a new hyperspectral unmixing method for nonlinearly mixed hyperspectral data using a semantic representation in a semi-supervised fashion, assuming the availability of a spectral reference library. Existing semi-supervised unmixing algorithms select members from an endmember library that are present at each of the pixels; most such methods assume a linear mixing model. However, those methods will fail in the presence of nonlinear mixing among the observed spectra. To address this issue, we develop an endmember selection method using a recently proposed semantic spectral representation obtained via non-homogeneous hidden Markov chain (NHMC) model for a wavelet transform of the spectra. The semantic representation can encode spectrally discriminative features for any observed spectrum and, therefore, our proposed method can perform endmember selection without any assumption on the mixing model. Experimental results show that in the presence of sufficiently nonlinear mixing our proposed method outperforms dictionary-based sparse unmixing approaches based on linear models.

cs.CV↗

arXiv2016

Perfect Recovery Conditions For Non-Negative Sparse Modeling

Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition. Accompanied with those applications, significant research has studied the theoretical limits and algorithm design for convex relaxations in sparse modeling. However, theoretical analyses on non-negative versions of sparse modeling are limited in the literature either to a noiseless setting or a scenario with a specific statistical noise model such as Gaussian noise. This paper studies the performance of non-negative sparse modeling in a more general scenario where the observed signals have an unknown arbitrary distortion, especially focusing on non-negativity constrained and L1-penalized least squares, and gives an exact bound for which this problem can recover the correct signal elements. We pose two conditions to guarantee the correct signal recovery: minimum coefficient condition (MCC) and nonlinearity vs. subset coherence condition (NSCC). The former defines the minimum weight for each of the correct atoms present in the signal and the latter defines the tolerable deviation from the linear model relative to the positive subset coherence (PSC), a novel type of "coherence" metric. We provide rigorous performance guarantees based on these conditions and experimentally verify their precise predictive power in a hyperspectral data unmixing application.

cs.IT↗

arXiv2016

Conditioning of Random Block Subdictionaries with Applications to Block-Sparse Recovery and Regression

The linear model, in which a set of observations is assumed to be given by a linear combination of columns of a matrix, has long been the mainstay of the statistics and signal processing literature. One particular challenge for inference under linear models is understanding the conditions on the dictionary under which reliable inference is possible. This challenge has attracted renewed attention in recent years since many modern inference problems deal with the "underdetermined" setting, in which the number of observations is much smaller than the number of columns in the dictionary. This paper makes several contributions for this setting when the set of observations is given by a linear combination of a small number of groups of columns of the dictionary, termed the "block-sparse" case. First, it specifies conditions on the dictionary under which most block subdictionaries are well conditioned. This result is fundamentally different from prior work on block-sparse inference because (i) it provides conditions that can be explicitly computed in polynomial time, (ii) the given conditions translate into near-optimal scaling of the number of columns of the block subdictionaries as a function of the number of observations for a large class of dictionaries, and (iii) it suggests that the spectral norm and the quadratic-mean block coherence of the dictionary (rather than the worst-case coherences) fundamentally limit the scaling of dimensions of the well-conditioned block subdictionaries. Second, this paper investigates the problems of block-sparse recovery and block-sparse regression in underdetermined settings. Near-optimal block-sparse recovery and regression are possible for certain dictionaries as long as the dictionary satisfies easily computable conditions and the coefficients describing the linear combination of groups of columns can be modeled through a mild statistical prior.

math.ST↗

arXiv2016

Masking Strategies for Image Manifolds

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the power expense grows with the number of pixels acquired. Our goal is for the manifold learned from masked images to resemble its full image counterpart as closely as possible. More precisely, we show that one can indeed accurately learn an image manifold without having to consider a large majority of the image pixels. In doing so, we consider two masking methods that preserve the local and global geometric structure of the manifold, respectively. In each case, the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated by a fast greedy algorithm. Numerical experiments show that the relevant manifold structure is preserved through the data-dependent masking process, even for modest mask sizes.

stat.ML↗

arXiv2016

Wavelet-Based Semantic Features for Hyperspectral Signature Discrimination

Hyperspectral signature classification is a quantitative analysis approach for hyperspectral imagery which performs detection and classification of the constituent materials at the pixel level in the scene. The classification procedure can be operated directly on hyperspectral data or performed by using some features extracted from the corresponding hyperspectral signatures containing information like the signature's energy or shape. In this paper, we describe a technique that applies non-homogeneous hidden Markov chain (NHMC) models to hyperspectral signature classification. The basic idea is to use statistical models (such as NHMC) to characterize wavelet coefficients which capture the spectrum semantics (i.e., structural information) at multiple levels. Experimental results show that the approach based on NHMC models can outperform existing approaches relevant in classification tasks.

cs.CV↗

arXiv2015

Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation

We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non-negative amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch between the manifold described by the parameters and its polar approximation. To quantify the improvements afforded by the proposed extensions, we evaluate six algorithms for estimation of parameters in sparse translation-invariant signals, exemplified with the time delay estimation problem. The evaluation is based on three performance metrics: estimator precision, sampling rate and computational complexity. We use compressive sensing with all the algorithms to lower the necessary sampling rate and show that it is still possible to attain good estimation precision and keep the computational complexity low. Our numerical experiments show that the proposed algorithms outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to a frequency-estimation problem followed by a super-resolution algorithm. The algorithms studied here provide various tradeoffs between computational complexity, estimation precision, and necessary sampling rate. The work shows that compressive sensing for the class of sparse translation-invariant signals allows for a decrease in sampling rate and that the use of polar interpolation increases the estimation precision.

cs.IT↗

arXiv2014

Recovery from Linear Measurements with Complexity-Matching Universal Signal Estimation

We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a stationary ergodic signal source are estimated simultaneously with the signal itself. Inspired by Kolmogorov complexity and minimum description length, we focus on a maximum a posteriori (MAP) estimation framework that leverages universal priors to match the complexity of the source. Our framework can also be applied to general linear inverse problems where more measurements than in CS might be needed. We provide theoretical results that support the algorithmic feasibility of universal MAP estimation using a Markov chain Monte Carlo implementation, which is computationally challenging. We incorporate some techniques to accelerate the algorithm while providing comparable and in many cases better reconstruction quality than existing algorithms. Experimental results show the promise of universality in CS, particularly for low-complexity sources that do not exhibit standard sparsity or compressibility.

cs.IT↗