Unmixing Results Research Articles

Multiobjective sparse unmixing based hyperspectral change detection

Hyperspectral unmixing can provide the composition of ground objects, while change detection can identify the changes of the same region over time. Therefore, unmixing based hyperspectral change detection can investigate changes in a subpixel-level. It can provide not only whether the change happens or not but also how to change. This paper will gradually establish an unconstrained sparse unmixing based change detection model and design a multiobjective optimization sparse unmixing approach (termed MoSU-CD) to solve it for more subpixel-level change details. Compared with the existing sparse unmixing based change detection approaches, MoSU-CD directly unmixes the difference map of multi-temporal images rather than multi-temporal images themselves respectively. Then it explores the change details of one substance in each pixel based on the unmixing results, i.e., endmembers and abundances. In addition, in order to improve the change detection accuracy, an ensemble decision strategy is designed for the Pareto optimal solutions obtained by multiobjective optimization method. Based on this strategy, the subpixel-level changes can be aggregated to generate an aggressive pixel-level change map. The experimental results on synthetic and real data sets demonstrate that the proposed MoSU-CD not only outperforms the benchmark and state-of-art approaches in terms of pixel-level change detection but also provides additional subpixel-level change information.

Robust hyperspectral unmixing using weighted group sparsity and minimum volume regularization

ABSTRACT Hyperspectral unmixing (HU) has been a vital technique in hyperspectral image processing. Over the past years, many algorithms have been developed based on the nonnegative matrix factorization (NMF) framework. However, the conventional methods based on the NMF need prior information of the number of endmembers, which is usually estimated by a separate procedure. Therefore, the precision of estimating the number of endmembers will impact the subsequent unmixing effect. Thus, collaborating between the two processes is desired to avoid the propagation of errors. This paper proposes a new NMF-based method, which can estimate the number of endmembers and extract the endmembers and the abundance maps. Firstly, we introduce the weighted group sparsity regularization to adaptively eliminate the abundances corresponding to the redundant endmembers, while the abundances of the true endmembers are preserved. Then the number of endmembers can be determined by the reconstruction error function and the l 2 -norm of the abundance vectors. Secondly, since the simplex determined by the endmembers has the minimum volume among all simplexes that circumscribe the data points, we impose the total variational regularization to force the endmembers to be close to each other to minimize the simplex volume. And because the total variational regularization avoids the use of noisy pixels, it can decrease the influence of noise and improve the robustness of the solution. For the proposed model, we design an effective algorithm to solve it. Also, the experimental results based on the synthetic data and real data demonstrate that the proposed method can identify the endmembers number well and achieve robust unmixing results.

Hyperspectral Blind Unmixing Using a Double Deep Image Prior.

With the rise of machine learning, hyperspectral image (HSI) unmixing problems have been tackled using learning-based methods. However, physically meaningful unmixing results are not guaranteed without proper guidance. In this work, we propose an unsupervised framework inspired by deep image prior (DIP) that can be used for both linear and nonlinear blind unmixing models. The framework consists of three modules: 1) an Endmember estimation module using DIP (EDIP); 2) an Abundance estimation module using DIP (ADIP); and 3) a mixing module (MM). EDIP and ADIP modules generate endmembers and abundances, respectively, while MM produces a reconstruction of the HSI observations based on the postulated unmixing model. We introduce a composite loss function that applies to both linear and nonlinear unmixing models to generate meaningful unmixing results. In addition, we propose an adaptive loss weight strategy for better unmixing results in nonlinear mixing scenarios. The proposed methods outperform state-of-the-art unmixing algorithms in extensive experiments conducted on both synthetic and real datasets.

Effects of skin tone on photoacoustic imaging and oximetry.

Photoacoustic imaging (PAI) provides contrast based on the concentration of optical absorbers in tissue, enabling the assessment of functional physiological parameters such as blood oxygen saturation (). Recent evidence suggests that variation in melanin levels in the epidermis leads to measurement biases in optical technologies, which could potentially limit the application of these biomarkers in diverse populations. To examine the effects of skin melanin pigmentation on PAI and oximetry. We evaluated the effects of skin tone in PAI using a computational skin model, two-layer melanin-containing tissue-mimicking phantoms, and mice of a consistent genetic background with varying pigmentations. The computational skin model was validated by simulating the diffuse reflectance spectrum using the adding-doubling method, allowing us to assign our simulation parameters to approximate Fitzpatrick skin types. Monte Carlo simulations and acoustic simulations were run to obtain idealized photoacoustic images of our skin model. Photoacoustic images of the phantoms and mice were acquired using a commercial instrument. Reconstructed images were processed with linear spectral unmixing to estimate blood oxygenation. Linear unmixing results were compared with a learned unmixing approach based on gradient-boosted regression. Our computational skin model was consistent with representative literature for in vivo skin reflectance measurements. We observed consistent spectral coloring effects across all model systems, with an overestimation of and more image artifacts observed with increasing melanin concentration. The learned unmixing approach reduced the measurement bias, but predictions made at lower blood still suffered from a skin tone-dependent effect. PAI demonstrates measurement bias, including an overestimation of blood , in higher Fitzpatrick skin types. Future research should aim to characterize this effect in humans to ensure equitable application of the technology.

Unsupervised Nonlinear Hyperspectral Unmixing with Reduced Spectral Variability via Superpixel-Based Fisher Transformation

In hyperspectral unmixing, dealing with nonlinear mixing effects and spectral variability (SV) is a significant challenge. Traditional linear unmixing can be seriously deteriorated by the coupled residuals of nonlinearity and SV in remote sensing scenarios. For the simplification of calculation, current unmixing studies usually separate the consideration of nonlinearity and SV. As a result, errors individually caused by the nonlinearity or SV still persist, potentially leading to overfitting and the decreased accuracy of estimated endmembers and abundances. In this paper, a novel unsupervised nonlinear unmixing method accounting for SV is proposed. First, an improved Fisher transformation scheme is constructed by combining an abundance-driven dynamic classification strategy with superpixel segmentation. It can enlarge the differences between different types of pixels and reduce the differences between pixels corresponding to the same class, thereby reducing the influence of SV. Besides, spectral similarity can be well maintained in local homogeneous regions. Second, the polynomial postnonlinear model is employed to represent observed pixels and explain nonlinear components. Regularized by a Fisher transformation operator and abundances’ spatial smoothness, data reconstruction errors in the original spectral space and the transformed space are weighed to derive the unmixing problem. Finally, this problem is solved by a dimensional division-based particle swarm optimization algorithm to produce accurate unmixing results. Extensive experiments on synthetic and real hyperspectral remote sensing data demonstrate the superiority of the proposed method in comparison with state-of-the-art approaches.

Projection subspace based low-rank representation for sparse hyperspectral unmixing

With a known large spectral library, sparse hyperspectral unmixing has been taken as a hotspot in academia all these years. Its fundamental task is to estimate the abundance fractions of the spectral signatures in mixed pixels. Typically, the sparse and low-rank properties of the abundance matrix have been exploited simultaneously in the literature. Many studies only consider the low-rank property of the entire abundance matrix, however, pay less attention to the property of each abundance map. In this paper, we propose a new way to describe the low-rank prior. Firstly, an abundance cube is obtained by concatenating the abundance maps along the third dimension. We construct a lower-dimensional projection subspace of the abundance cube using a projection matrix, and the low-rankness of the abundance matrix is preserved during the projection process. Secondly, we consider the low-rank property by directly analyzing the abundance maps in the projection subspace. Finally, two algorithms, namely: projection subspace low-rank structure for sparse unmixing and projection subspace low-rank structure for bilateral sparse unmixing, are proposed based on different sparse structures of the abundance matrix. Both simulated and real-data experiments demonstrate that compared with classical sparse unmixing algorithms, the proposed ones obtain better unmixing results as well as cut down on calculation time.

AutoUnmix: an autoencoder-based spectral unmixing method for multi-color fluorescence microscopy imaging.

Multiplexed fluorescence microscopy imaging is widely used in biomedical applications. However, simultaneous imaging of multiple fluorophores can result in spectral leaks and overlapping, which greatly degrades image quality and subsequent analysis. Existing popular spectral unmixing methods are mainly based on computational intensive linear models, and the performance is heavily dependent on the reference spectra, which may greatly preclude its further applications. In this paper, we propose a deep learning-based blindly spectral unmixing method, termed AutoUnmix, to imitate the physical spectral mixing process. A transfer learning framework is further devised to allow our AutoUnmix to adapt to a variety of imaging systems without retraining the network. Our proposed method has demonstrated real-time unmixing capabilities, surpassing existing methods by up to 100-fold in terms of unmixing speed. We further validate the reconstruction performance on both synthetic datasets and biological samples. The unmixing results of AutoUnmix achieve the highest SSIM of 0.99 in both three- and four-color imaging, with nearly up to 20% higher than other popular unmixing methods. For experiments where spectral profiles and morphology are akin to simulated data, our method realizes the quantitative performance demonstrated above. Due to the desirable property of data independency and superior blind unmixing performance, we believe AutoUnmix is a powerful tool for studying the interaction process of different organelles labeled by multiple fluorophores.

Spatial Validation of Spectral Unmixing Results: A Systematic Review

The pixels of remote images often contain more than one distinct material (mixed pixels), and so their spectra are characterized by a mixture of spectral signals. Since 1971, a shared effort has enabled the development of techniques for retrieving information from mixed pixels. The most analyzed, implemented, and employed procedure is spectral unmixing. Among the extensive literature on the spectral unmixing, nineteen reviews were identified, and each highlighted the many shortcomings of spatial validation. Although an overview of the approaches used to spatially validate could be very helpful in overcoming its shortcomings, a review of them was never provided. Therefore, this systematic review provides an updated overview of the approaches used, analyzing the papers that were published in 2022, 2021, and 2020, and a dated overview, analyzing the papers that were published not only in 2011 and 2010, but also in 1996 and 1995. The key criterion is that the results of the spectral unmixing were spatially validated. The Web of Science and Scopus databases were searched, using all the names that were assigned to spectral unmixing as keywords. A total of 454 eligible papers were included in this systematic review. Their analysis revealed that six key issues in spatial validation were considered and differently addressed: the number of validated endmembers; sample sizes and sampling designs of the reference data; sources of the reference data; the creation of reference fractional abundance maps; the validation of the reference data with other reference data; the minimization and evaluation of the errors in co-localization and spatial resampling. Since addressing these key issues enabled the authors to overcome some of the shortcomings of spatial validation, it is recommended that all these key issues be addressed together. However, few authors addressed all the key issues together, and many authors did not specify the spatial validation approach used or did not adequately explain the methods employed.

SSANet: An Adaptive Spectral–Spatial Attention Autoencoder Network for Hyperspectral Unmixing

Convolutional neural-network-based autoencoders, which can integrate the spatial correlation between pixels well, have been broadly used for hyperspectral unmixing and obtained excellent performance. Nevertheless, these methods are hindered in their performance by the fact that they treat all spectral bands and spatial information equally in the unmixing procedure. In this article, we propose an adaptive spectral–spatial attention autoencoder network, called SSANet, to solve the mixing pixel problem of the hyperspectral image. First, we design an adaptive spectral–spatial attention module, which refines spectral–spatial features by sequentially superimposing the spectral attention module and spatial attention module. The spectral attention module is built to select useful spectral bands, and the spatial attention module is designed to filter spatial information. Second, SSANet exploits the geometric properties of endmembers in the hyperspectral image while considering abundance sparsity. We significantly improve the endmember and abundance results by introducing minimum volume and sparsity regularization terms into the loss function. We evaluate the proposed SSANet on one synthetic dataset and four real hyperspectral scenes, i.e., Samson, Jasper Ridge, Houston, and Urban. The results indicate that the proposed SSANet achieved competitive unmixing results compared with several conventional and advanced unmixing approaches with respect to the root mean square error and spectral angle distance.

Unmixing Biological Fluorescence Image Data with Sparse and Low-Rank Poisson Regression.

Multispectral biological fluorescence microscopy has enabled the identification of multiple targets in complex samples. The accuracy in the unmixing result degrades (1) as the number of fluorophores used in any experiment increases and (2) as the signal-to-noise ratio in the recorded images decreases. Further, the availability of prior knowledge regarding the expected spatial distributions of fluorophores in images of labeled cells provides an opportunity to improve the accuracy of fluorophore identification and abundance. We propose a regularized sparse and low-rank Poisson unmixing approach (SL-PRU) to deconvolve spectral images labeled with highly overlapping fluorophores which are recorded in low signal-to-noise regimes. Firstly, SL-PRU implements multi-penalty terms when pursuing sparseness and spatial correlation of the resulting abundances in small neighborhoods simultaneously. Secondly, SL-PRU makes use of Poisson regression for unmixing instead of least squares regression to better estimate photon abundance. Thirdly, we propose a method to tune the SL-PRU parameters involved in the unmixing procedure in the absence of knowledge of the ground truth abundance information in a recorded image. By validating on simulated and real-world images, we show that our proposed method leads to improved accuracy in unmixing fluorophores with highly overlapping spectra. The source code used for this paper was written in MATLAB and is available with the test data at https://github.com/WANGRUOGU/SL-PRU. Supplementary data are available at Bioinformatics online.

Endmembers compression based nonnegative matrix factorization for hyperspectral unmixing

ABSTRACT Hyperspectral unmixing (HU) has grown more important in hyperspectral images (HSIs) research in recent years. Many models based on nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF) have been extensively used to tackle the HU problem. Most of these models allow a large and extensive exploration of abundance and provide promising unmixing results. However, the exploration of each endmember information is insufficient. In this article, we propose an unmixing model called endmembers compressionbased NMF (EC-NMF) for HU. Specifically, by an orthogonal projection, the EC-NMF enables distinct endmembers to be differentiated from each other. In this space, each compressed endmember represents the distinct characteristics of the corresponding endmember, which makes it easier for the endmembers separated. Furthermore, the EC-NMF model incorporates the reweighted nuclear norm on the abundance map to fully account for spatial information and to constrain its low-rank properties. The EC-NMF model is solved by an augmented multiplicative algorithm. In particular, we achieve the proposed model based on the matrix representation, which reduces the computational complexity compared with NTF-based methods. Extensive experiments on synthetic and real data give concrete evidence that the proposed method outperforms other known methods in both the unmixing performance and running time.

LANDSAT multispectral image analysis of bedrock exposure rate in highly heterogeneous karst areas through mixed pixel decomposition considering spectral variability

AbstractMixed pixels and spectral variations commonly occur in images of karst areas because these areas have rugged topography and high surface heterogeneity. Consequently, the bedrock exposure rate cannot be accurately estimated using the existing rock index method based on remote sensing and the fixed endmember mixed pixel decomposition model. In order to solve this problem, using LANDSAT operational land imager/thematic mapper (OLI/TM) images as the data source, this study estimated the bedrock exposure rate based on a generalized linear mixed model (GLMM) considering spectral variability. In addition, this approach was compared with existing commonly used methods for estimating bedrock exposure rate. The results show that: (1) GLMM showed the highest performance in estimating bedrock exposure rate, with a total accuracy of 88.05% and a kappa coefficient of 0.845, and the accuracy exceeded 70% for different levels of bedrock exposure rate. However, the total accuracy of other commonly used bedrock exposure methods is was below 66%, being higher only in areas with bedrock exposure rates less than 20% and more than 70%. (2) By applying each method to different terrain scenes, GLMM was found to be more stable than other methods, and the estimated bedrock exposure rate is the closest to the ground reference value with a root mean square error less than 0.093. Other methods, including fully constrained least squares unmixing (FCLSU) and karst bare‐rock index (KBRI), have a certain gap in different scenes, and their accuracy is not high. (3) Without any ground reference data, the accuracy of the direct unmixing result of GLMM is very close to that calculated by the regression model, and the accuracy difference among different grades of bedrock exposure rate is less than 5%, thus outperforming the other methods. GLMM can effectively estimate the bedrock exposure rate at different times using different data. Therefore, GLMM has great potential in extracting rocky desertification information in karst areas. It can also be a reference method for the rapid, accurate, and long‐term evaluation of rocky desertification in karst areas.

Blind Hyperspectral Unmixing with Enhanced 2DTV Regularization Term

For the problem where the existing hyperspectral unmixing methods do not take full advantage of the correlations and differences between all these bands, resulting in affecting the final unmixing results, we design an enhanced 2DTV (E-2DTV) regularization term and suggest a blind hyperspectral unmixing method with the E-2DTV regularization term (E-gTVMBO), which adds E-2DTV regularization to the previous blind hyperspectral unmixing based on g-TV model. The E-2DTV regularization term is based on the gradient mapping of all bands of HSI, and the sparsity is calculated on the basis of the subspace, rather than applying sparsity to the gradient map itself, which can utilize the correlations and differences between all bands naturally. The experimental results prove the superiority of the E-gTVMBO method from both qualitative and quantitative perspectives. The research results can be applied to land cover classification, mineral analysis, and other fields.

Arctic sea ice melt pond fraction in 2000–2021 derived by dynamic pixel spectral unmixing of MODIS images

The Arctic has experienced extensive sea ice retreat in recent decades, as observed from satellite remote sensing and simulated by general circulation models. The significant low albedo of melt pond compared with snow and ice results in more absorption of radiation compared with sea ice without melt pond, which will then enhance sea ice melt to form more melt pond. This so-called positive feedback of melt pond is crucial for sea ice thermal and physical properties. The melt pond coverage varies significantly spatially and temporally and satellite remote sensing provides a possible solution in determining the spatial coverage of melt pond. This work aims to develop a new physically based algorithm for retrieving the cover fraction of melt ponds on sea ice using remote sensing data. In the newly developed algorithm, dynamic sea ice and melt pond reflectances are used in the pixel spectral unmixing for melt pond fraction (MPF) estimation. Radiative transfer models for sea ice and melt pond reflectance modeling are developed for MPF retrieval algorithm. The validation of retrieved MPF and its comparison with static pixel spectral unmixing results show that the dynamic algorithm proposed in this study has the potential of application in wide range of situations by considering dynamic spectral reflectances of melt pond and sea ice. The Arctic MPF and sea ice cover fraction (SIF) in 2000–2021 are generated by applying the proposed algorithm. The spatial and temporal characteristics of MPF and SIF are analyzed. Time series trend analysis of MPF in 2000–2021 reveals the significant increasing trend of relative MPF in the Arctic. The melt pond expansion in 2000–2021 is more obvious in the marginal areas, especially the marginal areas close to Russia coast. Trend analysis for typical regions such as Beaufort Sea, Greenland Sea, the Baffin Bay, Chukchi, East Siberian, Laptev, and Kara seas and center Arctic also reveals that the relative MPF and SIF show contrasting trend.

SUFI: an automated approach to spectral unmixing of fluorescent multiplex images captured in mouse and post-mortem human brain tissues

BackgroundMultispectral fluorescence imaging coupled with linear unmixing is a form of image data collection and analysis that allows for measuring multiple molecular signals in a single biological sample. Multiple fluorescent dyes, each measuring a unique molecule, are simultaneously measured and subsequently “unmixed” to provide a read-out for each molecular signal. This strategy allows for measuring highly multiplexed signals in a single data capture session, such as multiple proteins or RNAs in tissue slices or cultured cells, but can often result in mixed signals and bleed-through problems across dyes. Existing spectral unmixing algorithms are not optimized for challenging biological specimens such as post-mortem human brain tissue, and often require manual intervention to extract spectral signatures. We therefore developed an intuitive, automated, and flexible package called SUFI: spectral unmixing of fluorescent images.ResultsThis package unmixes multispectral fluorescence images by automating the extraction of spectral signatures using vertex component analysis, and then performs one of three unmixing algorithms derived from remote sensing. We evaluate these remote sensing algorithms’ performances on four unique biological datasets and compare the results to unmixing results obtained using ZEN Black software (Zeiss). We lastly integrate our unmixing pipeline into the computational tool dotdotdot, which is used to quantify individual RNA transcripts at single cell resolution in intact tissues and perform differential expression analysis, and thereby provide an end-to-end solution for multispectral fluorescence image analysis and quantification.ConclusionsIn summary, we provide a robust, automated pipeline to assist biologists with improved spectral unmixing of multispectral fluorescence images.

Binary Change Guided Hyperspectral Multiclass Change Detection.

Characterized by tremendous spectral information, hyperspectral image is able to detect subtle changes and discriminate various change classes for change detection. The recent research works dominated by hyperspectral binary change detection, however, cannot provide fine change classes information. And most methods incorporating spectral unmixing for hyperspectral multiclass change detection (HMCD), yet suffer from the neglection of temporal correlation and error accumulation. In this study, we proposed an unsupervised Binary Change Guided hyperspectral multiclass change detection Network (BCG-Net) for HMCD, which aims at boosting the multiclass change detection result and unmixing result with the mature binary change detection approaches. In BCG-Net, a novel partial-siamese united-unmixing module is designed for multi-temporal spectral unmixing, and a groundbreaking temporal correlation constraint directed by the pseudo-labels of binary change detection result is developed to guide the unmixing process from the perspective of change detection, encouraging the abundance of the unchanged pixels more coherent and that of the changed pixels more accurate. Moreover, an innovative binary change detection rule is put forward to deal with the problem that traditional rule is susceptible to numerical values. The iterative optimization of the spectral unmixing process and the change detection process is proposed to eliminate the accumulated errors and bias from unmixing result to change detection result. The experimental results demonstrate that our proposed BCG-Net could achieve comparative or even outstanding performance of multiclass change detection among the state-of-the-art approaches and gain better spectral unmixing results at the same time.

Adaptive Hypergraph Regularized Multilayer Sparse Tensor Factorization for Hyperspectral Unmixing

Hyperspectral unmixing with tensor models has received great attention in recent years. A tensor-based decomposition method can effectively represent the structural feature of hyperspectral images; however, the obtained results may be physically uninterpretable. To overcome this limitation, a novel adaptive hypergraph regularized multilayer sparse tensor factorization (AHGMLSTF) algorithm is proposed. First, a modified hypergraph is incorporated into tensor factorization, and the modified hypergraph uses spectral angle distance (SAD) instead of Euclidean distance to construct hyperedges to better represent the joint spatial and spectral information. Then, the hypergraph is constructed adaptively by hyperedges of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> neighborhoods. Second, the concept of multilayer decomposition is introduced to explore the hierarchical features of hyperspectral images, and a sparse constraint is imposed on each layer to make the unmixing results more consistent with the physical mechanism of mixed spectral pixels. With these constraints, the proposed method established a spectral–spatial joint tensor decomposition model that represents not only the local neighborhood similarity but also the heterogeneity of adjacent edges. Experiments on simulated data and real hyperspectral data demonstrate the effectiveness of the proposed method.

IVIU-Net: Implicit Variable Iterative Unrolling Network for Hyperspectral Sparse Unmixing

At present, an emerging technique called the algorithm unrolling approach has attracted wide attention, because it is capable of developing efficient and interpretable layers to eliminate the black-box nature of deep learning (DL). In this paper, inspired by the sparse unmixing model, we propose a model-driven DL approach, namely, an implicit variable iterative unrolling network (IVIU-Net). First of all, the unmixing performance and adaptive ability of the model are enhanced by introducing learnable parameters into the sparse unmixing algorithm. Then, a specific spatial convolution module is integrated into the network to promote the smoothness of the latent abundance map. Finally, a comprehensive loss function with three terms such as average spectral angle distance, HSIs reconstruction error, and spectral information divergence, is presented to train the IVIU-Net in an unsupervised way. Compared to the unmixing results of most existing data-driven DL algorithms, our network has significant advantages in two folds: 1) it is able to achieve better stability instead of relying heavily on the endmember initialization results; 2) it has better interpretability and robustness in the unmixing procedure. Experimental results on synthetic and real data show that the proposed network outperforms the state-of-the-art in terms of better convergence, faster unmixing speed as well as better accuracy.

Motion Compensation for 3D Multispectral Handheld Photoacoustic Imaging.

Three-dimensional (3D) handheld photoacoustic (PA) and ultrasound (US) imaging performed using mechanical scanning are more useful than conventional 2D PA/US imaging for obtaining local volumetric information and reducing operator dependence. In particular, 3D multispectral PA imaging can capture vital functional information, such as hemoglobin concentrations and hemoglobin oxygen saturation (sO2), of epidermal, hemorrhagic, ischemic, and cancerous diseases. However, the accuracy of PA morphology and physiological parameters is hampered by motion artifacts during image acquisition. The aim of this paper is to apply appropriate correction to remove the effect of such motion artifacts. We propose a new motion compensation method that corrects PA images in both axial and lateral directions based on structural US information. 3D PA/US imaging experiments are performed on a tissue-mimicking phantom and a human wrist to verify the effects of the proposed motion compensation mechanism and the consequent spectral unmixing results. The structural motions and sO2 values are confirmed to be successfully corrected by comparing the motion-compensated images with the original images. The proposed method is expected to be useful in various clinical PA imaging applications (e.g., breast cancer, thyroid cancer, and carotid artery disease) that are susceptible to motion contamination during multispectral PA image analysis.

Spatial Validation of Spectral Unmixing Results: A Case Study of Venice City

Since remote sensing images offer unique access to the distribution of land cover on earth, many countries are investing in this technique to monitor urban sprawl. For this purpose, the most widely used methodology is spectral unmixing which, after identifying the spectra of the mixed-pixel constituents, determines their fractional abundances in the pixel. However, the literature highlights shortcomings in spatial validation due to the lack of detailed ground truth knowledge and proposes five key requirements for accurate reference fractional abundance maps: they should cover most of the area, their spatial resolution should be higher than that of the results, they should be validated using other ground truth data, the full range of abundances should be validated, and errors in co-localization and spatial resampling should be minimized. However, most proposed reference maps met two or three requirements and none met all five. In situ and remote data acquired in Venice were exploited to meet all five requirements. Moreover, to obtain more information about the validation procedure, not only reference spectra, synthetic image, and fractional abundance models (FAMs) that met all the requirements, but also other data, that no previous work exploited, were employed: reference fractional abundance maps that met four out of five requirements, and fractional abundance maps retrieved from the synthetic image. Briefly summarizing the main results obtained from MIVIS data, the average of spectral accuracies in root mean square error was equal to 0.025; using FAMs, the average of spatial accuracies in mean absolute error (MAEk-Totals) was equal to 1.32 and more than 78% of these values were related to sensor characteristics; using reference fractional abundance maps, the average MAEk-Totals value increased to 1.97 because errors in co-localization and spatial-resampling affected about 29% of these values. In conclusion, meeting all requirements and the exploitation of different reference data increase the spatial accuracy, upgrade the validation procedure, and improve the knowledge of accuracy.