nils-herrmann/clean_scirepeval huggingface dataset:
Restoration of Poissonian Images Using Alternating Direction Optimization

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based upon multiscale representations or total variation) is still an active research area, since the associated optimization problems are quite challenging. In this paper, we propose an approach to deconvolving Poissonian images, which is based upon an alternating direction optimization method. The standard regularization [or maximum a posteriori (MAP)] restoration criterion, which combines the Poisson log-likelihood with a (nonsmooth) convex regularizer (log-prior), leads to hard optimization problems: the log-likelihood is nonquadratic and nonseparable, the regularizer is nonsmooth, and there is a nonnegativity constraint. Using standard convex analysis tools, we present sufficient conditions for existence and uniqueness of solutions of these optimization problems, for several types of regularizers: total-variation, frame-based analysis, and frame-based synthesis. We attack these problems with an instance of the alternating direction method of multipliers (ADMM), which belongs to the family of augmented Lagrangian algorithms. We study sufficient conditions for convergence and show that these are satisfied, either under total-variation or frame-based (analysis and synthesis) regularization. The resulting algorithms are shown to outperform alternative state-of-the-art methods, both in terms of speed and restoration accuracy.
Fusing Hyperspectral and Multispectral Images via Coupled Sparse Tensor Factorization

Fusing a low spatial resolution hyperspectral image (LR-HSI) with a high spatial resolution multispectral image (HR-MSI) to obtain a high spatial resolution hyperspectral image (HR-HSI) has attracted increasing interest in recent years. In this paper, we propose a coupled sparse tensor factorization (CSTF)-based approach for fusing such images. In the proposed CSTF method, we consider an HR-HSI as a 3D tensor and redefine the fusion problem as the estimation of a core tensor and dictionaries of the three modes. The high spatial-spectral correlations in the HR-HSI are modeled by incorporating a regularizer, which promotes sparse core tensors. The estimation of the dictionaries and the core tensor are formulated as a coupled tensor factorization of the LR-HSI and of the HR-MSI. Experiments on two remotely sensed HSIs demonstrate the superiority of the proposed CSTF algorithm over the current state-of-the-art HSI-MSI fusion approaches.
An augmented Lagrangian approach to linear inverse problems with compound regularization

In some imaging inverse problems, it may be desired that the solution simultaneously exhibits a set of properties not enforceable by a single regularizer. To attain this goal, one may use a linear combinations of regularizers, thus encouraging the solution to simultaneously exhibit the characteristics enforced by each of them. This paper addresses the optimization problem associated with this type of compound regularization, using an alternating direction optimization algorithm. We illustrate the approach in two image deblurring problems - one in which the images are simultaneously sparse and piece-wise smooth, using a linear combination of the ℓ1 and total variation regularizers, and the other for a natural image with a combination of frame-based synthesis and analysis ℓ1 norm regularizers.
Effect of Denoising in Band Selection for Regression Tasks in Hyperspectral Datasets

This paper presents a comparative analysis of six band selection methods applied to hyperspectral datasets for biophysical variable estimation problems, where the effect of denoising on band selection performance has also been analyzed. In particular, we consider four hyperspectral datasets and three regressors of different nature (ε-SVR, Regression Trees, and Kernel Ridge Regression). Results show that the denoising approach improves the band selection quality of all the tested methods. We show that noise filtering is more beneficial for the selection methods that use an estimator based on the whole dataset for the prediction of the output than for methods that use strategies based on local information (neighboring points).
Convex Formulation for Multiband Image Classification With Superpixel-Based Spatial Regularization

Superpixels are a powerful device to characterize the spatial–contextual information in remotely sensed hyperspectral image (HSI) interpretation. However, the exploitation of superpixels in classification problems is not straightforward, often leading to unbearable NP-hard discrete integer optimization problems. In this paper, we attack this hurdle by leveraging on a convex relaxation of the original integer optimization problem, which opens the door to include oversegmented superpixel-based regularizers. Specifically, we develop a new method for generating oversegmented superpixels. Then, we introduce a family of convex regularizers in the form of graph total variation, which promotes the same labeling in each superpixel. Vectorial total variation is also included in order to promote piecewise smoothness and align discontinuities along the class boundaries. The solution of the obtained convex optimization problem is computed with the split-augmented Lagrangian shrinkage algorithm. Experiments on HSIs yield classification maps with precise boundaries and inner consistency inside oversegmented superpixels, leading to the state-of-the-art classification accuracies.
Parametric Blur Estimation for Blind Restoration of Natural Images: Linear Motion and Out-of-Focus

This paper presents a new method to estimate the parameters of two types of blurs, linear uniform motion (approximated by a line characterized by angle and length) and out-of-focus (modeled as a uniform disk characterized by its radius), for blind restoration of natural images. The method is based on the spectrum of the blurred images and is supported on a weak assumption, which is valid for the most natural images: the power-spectrum is approximately isotropic and has a power-law decay with the spatial frequency. We introduce two modifications to the radon transform, which allow the identification of the blur spectrum pattern of the two types of blurs above mentioned. The blur parameters are identified by fitting an appropriate function that accounts separately for the natural image spectrum and the blur frequency response. The accuracy of the proposed method is validated by simulations, and the effectiveness of the proposed method is assessed by testing the algorithm on real natural blurred images and comparing it with state-of-the-art blind deconvolution methods.
An iterative algorithm for linear inverse problems with compound regularizers

In several imaging inverse problems, it may be of interest to encourage the solution to have characteristics which are most naturally expressed by the combination of more than one regularizer. The resulting optimization problems can not be dealt with by the current state-of-the-art algorithms, which are designed for single regularizers (such as total variation or sparseness-inducing penalties, but not both simultaneously). In this paper, we introduce an iterative algorithm to solve the optimization problem resulting from image (or signal) inverse problems with two (or more) regularizers. We illustrate the new algorithm in a problem of restoration of "group sparse" images, i.e., images displaying a special type of sparseness in which the active pixels tend to cluster together. Experimental results show the effectiveness of the proposed algorithm in solving the corresponding optimization problem.
Source localization from time-differences of arrival using high-frequency communication signals

Localization of underwater acoustic (UWA) sources using observed signals is a popular research topic that has many potential applications, both military and civilian (e.g., navigation of underwater vehicles, mine hunting, marine mammal studies). This work adopts an inverse problem framework where the temporal and spatial structure of multipath observed at an array of sensors deployed in an ocean waveguide is exploited to determine the source position. The proposed method aims at deriving useful spatial information as side information from high-frequency signals used for underwater acoustic communication. The approach involves several steps: (i) estimating channel responses and segmenting wavefronts to recover the temporal and spatial structure of multipath arrivals at the receiver array; (ii) computing a coarse source position estimate with no a priori knowledge of its location and only crude environmental information; (iii) refining the source location using model-based tomographic methods that match observed vs. predicted wavefront arrival patterns across the array through ray tracing. The Coarse Source Localization (CSL) scheme uses an algorithm for free-space localization based on time differences of arrival, and several modifications are discussed to adapt it to non-homogeneous underwater waveguides. The ensuing Model-Based Source Localization (MBSL) scheme uses an iterative linearized least-squares algorithm and benefits from the good accuracy of CSL to attain very fast convergence and avoid local extrema of its multimodal cost function. The algorithms are tested in simulation and using experimental data (CALCOM'10) for high-frequency transmissions at ranges from 200 m to 1 km.
A fast algorithm for the constrained formulation of compressive image reconstruction and other linear inverse problems

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard formulation for dealing with ILIP consists in a constrained optimization problem, where a regularization function is minimized under the constraint that the solution explains the observations sufficiently well. The regularizer and constraint are usually convex; however, several particular features of these problems (huge dimensionality, non-smoothness) preclude the use of off-the-shelf optimization tools and have stimulated much research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the category of augmented Lagrangian methods, can be used to deal with a variety of imaging ILIP, including deconvolution and reconstruction from compressive observations (such as MRI). Experiments testify for the effectiveness of the proposed method.
Wavefront segmentation and classification for model-based underwater high-frequency tomography

The problem of inferring side information regarding an underwater acoustic (UWA) channel from the environmental signature imprinted on waveforms by the propagation medium, particularly the transmitter/receiver configuration and relative speed vector, is addressed in this paper. The main contribution of this work is to develop techniques to automatically deal with wavefront classification, i.e., to assign the appropriate number of surface and bottom bounces to a propagation path detected in the set of channel responses observed at a receiver array, considering possible omission or duplication of some paths. This is a key step to develop automatic and robust source localization and velocity estimation algorithms, which are also overviewed here. Our inference algorithms directly operate on linear time-varying UWA channel responses, represented as 3-dimensional delay-Doppler-depth functions (DDDF). At each depth a sparse delay-Doppler spread function (DDSF), analogous to the impulse response of time-invariant systems, is estimated using Basis-Pursuit (BP) methods. The ensemble is processed with energy-based methods to detect the spatio-temporal signatures of wavefronts, which are then matched to candidate environmental configurations by a parametric propagation model. The proposed approaches have been assessed using simulation and empirical data collected during the CALCOM'10 sea trial for various communication ranges from 300 m to 2 km and varying relative speed within the limit of 6 knots.
A robust subspace method for semiblind dictionary-aided hyperspectral unmixing

Recent development in semiblind dictionary-aided hyperspectral unmixing (HU) shows that a classical method in sensor array processing, namely, multiple signal classification (MUSIC), provides an effective way for endmember identification. However, MUSIC (and in fact, other dictionary-based sparse regression algorithms) assumes that there are no mismatches between the true endmember signatures and the dictionary spectral signatures, which may be violated in practice owing to reasons such as endmember variability and calibration errors. This paper presents a robust MUSIC method, wherein spectral signature mismatches are incorporated in the original MUSIC formulation to make the resulting algorithm robust. A computationally simple method is derived for the implementation of robust MUSIC. Simulation results show that robust MUSIC provides improved robustness against spectral signature mismatches than the original MUSIC.
Parallel implementation of vertex component analysis for hyperspectral endmember extraction

Vertex component analysis (VCA) has become a very popular and useful tool to linear unmix large hyperspectral datasets without the use of any a priori knowledge of the constituent spectra. Although VCA is fast method, many hyperspectral imagery applications require a response in real time or near-real time. This paper proposes two different optimizations for accelerating the computational performance of VCA: the first one focus a parallel implementation based on graphics computing units (GPUs) to alleviate the VCA computational burden; The second one is focused on the development of a strategy to remove a large proportion of mixed pixels that play no effect on the VCA functioning. Experiments are conducted using simulated and real hyperspectral datasets. These results reveal considerable acceleration factors, which satisfies the real-time constraints given by the data acquisition rate.
Phase Drift Estimation and Symbol Detection in Digital Communications: A Stochastic Recursive Filtering Approach

This paper proposes a novel Bayesian stochastic filtering approach for the simultaneous phase drift estimation and symbol detection in digital communications. The posterior density of the phase drift is propagated in a recursive fashion by implementing a prediction and a filtering step in each iteration. The prediction step is supported on a random walk model playing the role of prior for the phase drift process; the filtering step is supported on a Gaussian sum approximation for the probability density of the current observation, i.e., the so-called sensor factor. The Gaussian sum approximation turns out to be the key element allowing to derive a fast and efficient stochastic filter, which otherwise would be very hard to compute. The detection of the digital symbols is then carried out based on the inferred statistics of the phase drift. The effectiveness of the proposed method is illustrated for BPSK signals in the presence of strong phase drift.
MUSIC-CSR: Hyperspectral Unmixing via Multiple Signal Classification and Collaborative Sparse Regression

Spectral unmixing aims at finding the spectrally pure constituent materials (also called endmembers) and their respective fractional abundances in each pixel of a hyperspectral image scene. In recent years, sparse unmixing has been widely used as a reliable spectral unmixing methodology. In this approach, the observed spectral vectors are expressed as linear combinations of spectral signatures assumed to be known a priori and presented in a large collection, termed spectral library or dictionary, usually acquired in laboratory. Sparse unmixing has attracted much attention as it sidesteps two common limitations of classic spectral unmixing approaches, namely, the lack of pure pixels in hyperspectral scenes and the need to estimate the number of endmembers in a given scene, which are very difficult tasks. However, the high mutual coherence of spectral libraries, jointly with their ever-growing dimensionality, strongly limits the operational applicability of sparse unmixing. In this paper, we introduce a two-step algorithm aimed at mitigating the aforementioned limitations. The algorithm exploits the usual low dimensionality of the hyperspectral data sets. The first step, which is similar to the multiple signal classification array signal processing algorithm, identifies a subset of the library elements, which contains the endmember signatures. Because this subset has cardinality much smaller than the initial number of library elements, the sparse regression we are led to is much more well conditioned than the initial one using the complete library. The second step applies collaborative sparse regression, which is a form of structured sparse regression, exploiting the fact that only a few spectral signatures in the library are active. The effectiveness of the proposed approach, termed MUSIC-CSR, is extensively validated using both simulated and real hyperspectral data sets.
Total variation restoration of speckled images using a split-bregman algorithm

Multiplicative noise models occur in the study of several coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. This type of noise is also commonly referred to as speckle. Multiplicative noise introduces two additional layers of difficulties with respect to the popular Gaussian additive noise model: (1) the noise is multiplied by (rather than added to) the original image, and (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of the multiplicative noise model preclude the direct application of state-of-the-art restoration methods, such as those based on the combination of total variation or wavelet-based regularization with a quadratic observation term. In this paper, we tackle these difficulties by: (1) using the common trick of converting the multiplicative model into an additive one by taking logarithms, and (2) adopting the recently proposed split Bregman approach to estimate the underlying image under total variation regularization. This approach is based on formulating a constrained problem equivalent to the original unconstrained one, which is then solved using Bregman iterations (equivalently, an augmented Lagrangian method). A set of experiments show that the proposed method yields state-of-the-art results.
Identification and matching of sparse Delay-Doppler Spread Functions from high-frequency communications signals

This work proposes methods for estimating the responses of time-varying underwater acoustic channels using ℓ2 - ℓ1 basis pursuit and quantifying their similarity. This is motivated by problems where environmental information is to be extracted from communications signals through high-frequency ocean acoustic tomographic techniques. We view underwater channels as time-varying linear systems and characterize them by their Delay-Doppler Spread Functions (DDSF), which have many adjustable parameters but are often very sparse. Basis pursuit estimation of DDSF coefficients is achieved with either the SpaRSA or TwIST algorithms, which can efficiently handle sparse unconstrained ℓ2 - ℓ1 minimization even for very large problem sizes, and directly operate on the complex signals of baseband communication models. We show that these algorithms offer better performance than matching pursuit methods, in terms of DDSF estimation accuracy and computational complexity, using both simulated and real data. We examine criteria based on Euclidean distance, correlation, and Kullback-Leibler divergence for quantifying the similarity of DDSFs, as needed in the envisaged tomographic systems for matching observations and model predictions. Their performance is found to be similar, with the correlation metric showing somewhat less consistent performance than the other two in simulation. Our matching approach also enables a simplification of DDSF estimation algorithms by tolerating the inherent biasing in ℓ2 - ℓ1 solutions, and thereby avoiding the need for further postprocessing.
Hyperspectral Super-Resolution of Locally Low Rank Images From Complementary Multisource Data

Remote sensing hyperspectral images (HSIs) are quite often low rank, in the sense that the data belong to a low dimensional subspace/manifold. This has been recently exploited for the fusion of low spatial resolution HSI with high spatial resolution multispectral images in order to obtain super-resolution HSI. Most approaches adopt an unmixing or a matrix factorization perspective. The derived methods have led to state-of-the-art results when the spectral information lies in a low-dimensional subspace/manifold. However, if the subspace/manifold dimensionality spanned by the complete data set is large, i.e., larger than the number of multispectral bands, the performance of these methods mainly decreases because the underlying sparse regression problem is severely ill-posed. In this paper, we propose a local approach to cope with this difficulty. Fundamentally, we exploit the fact that real world HSIs are locally low rank, that is, pixels acquired from a given spatial neighborhood span a very low-dimensional subspace/manifold, i.e., lower or equal than the number of multispectral bands. Thus, we propose to partition the image into patches and solve the data fusion problem independently for each patch. This way, in each patch the subspace/manifold dimensionality is low enough, such that the problem is not ill-posed anymore. We propose two alternative approaches to define the hyperspectral super-resolution through local dictionary learning using endmember induction algorithms. We also explore two alternatives to define the local regions, using sliding windows and binary partition trees. The effectiveness of the proposed approaches is illustrated with synthetic and semi real data.
An Alternating Direction Algorithm for Total Variation Reconstruction of Distributed Parameters

Augmented Lagrangian variational formulations and alternating optimization have been adopted to solve distributed parameter estimation problems. The alternating direction method of multipliers (ADMM) is one of such formulations/optimization methods. Very recently, the number of applications of the ADMM, or variants of it, to solve inverse problems in image and signal processing has increased at an exponential rate. The reason for this interest is that ADMM decomposes a difficult optimization problem into a sequence of much simpler problems. In this paper, we use the ADMM to reconstruct piecewise-smooth distributed parameters of elliptical partial differential equations from noisy and linear (blurred) observations of the underlying field. The distributed parameters are estimated by solving an inverse problem with total variation (TV) regularization. The proposed instance of the ADMM solves, in each iteration, an and a decoupled optimization problems. An operator splitting is used to simplify the treatment of the TV regularizer, avoiding its smooth approximation and yielding a simple yet effective ADMM reconstruction method compared with previously proposed approaches. The competitiveness of the proposed method, with respect to the state-of-the-art, is illustrated in simulated 1-D and 2-D elliptical equation problems, which are representative of many real applications.