Sparse Data Acquisition Research Articles

Acoustic field visualization and source localization via physics-informed learning of sparse data with adaptive sampling

Traditional methods for acoustic field visualization require considerable effort for capturing large amounts of acoustic data to achieve a high resolution field map, highly limiting their widespread use. In this study, we propose an approach for acoustic field visualization based on physics-informed neural networks (PINNs) by using a small amount of data, subsequently realizing accurate acoustic source localization. First, we present a PINN model integrated with an acoustic Helmholtz equation and adaptive sampling, the performance of which is testified via numerical simulations. The “no mesh” character of PINN enables achieving high resolution acoustic field visualization without requiring the capture of numerous data in advance. Furthermore, we experimentally validate the performance of the proposed method, which demonstrates that the acoustic sources can be precisely localized with sparse field data acquisition within a small area. This work would find potential applications in various acoustics, such as acoustic communication, biomedical imaging, and virtual reality.

A novel sequential estimation framework for battery state of health and remaining useful life based on sparse and limited data

Battery State of Health (SOH) estimation and Remaining Useful Life (RUL) prediction are significant for battery management systems in both electric vehicles and energy storage systems. Various battery Health Indicators (HIs) and abundant health information are generally utilized for SOH and RUL estimation. However, HIs and health information may not be available for various reasons such as sensor installation limitations, computational burden and communication delay of the system. To overcome the issue of sparse and limited data acquisition in real applications, this study proposed a novel battery SOH and RUL sequential estimation framework only utilizing sparse segments of time series voltage data. The Extreme Learning Machine (ELM) and Long Short Term Memory (LSTM) network are applied for SOH estimation and RUL prediction respectively. Locally Weighted Scatterplot Smoothing (LOWESS) is used for both data smoothing and sparse data reconstruction. Three common battery datasets are fully investigated for validation. The experiment results show well estimation accuracies in both battery SOH and RUL, demonstrating the effectiveness of the framework in limited data prediction. Several popular SOH and RUL estimation algorithms and two state-of-the-art works are compared to further elaborate the superiority of the proposed framework.

Image to Label to Answer: An Efficient Framework for Enhanced Clinical Applications in Medical Visual Question Answering

Medical Visual Question Answering (Med-VQA) faces significant limitations in application development due to sparse and challenging data acquisition. Existing approaches focus on multi-modal learning to equip models with medical image inference and natural language understanding, but this worsens data scarcity in Med-VQA, hindering clinical application and advancement. This paper proposes the ITLTA framework for Med-VQA, designed based on field requirements. ITLTA combines multi-label learning of medical images with the language understanding and reasoning capabilities of large language models (LLMs) to achieve zero-shot learning, meeting natural language module needs without end-to-end training. This approach reduces deployment costs and training data requirements, allowing LLMs to function as flexible, plug-and-play modules. To enhance multi-label classification accuracy, the framework uses external medical image data for pretraining, integrated with a joint feature and label attention mechanism. This configuration ensures robust performance and applicability, even with limited data. Additionally, the framework clarifies the decision-making process for visual labels and question prompts, enhancing the interpretability of Med-VQA. Validated on the VQA-Med 2019 dataset, our method demonstrates superior effectiveness compared to existing methods, confirming its outstanding performance for enhanced clinical applications.

Research on 3D Visualization of Drone Scenes Based on Neural Radiance Fields

Neural Radiance Fields (NeRFs), as an innovative method employing neural networks for the implicit representation of 3D scenes, have been able to synthesize images from arbitrary viewpoints and successfully apply them to the visualization of objects and room-level scenes (<50 m2). However, due to the capacity limitations of neural networks, the rendering of drone-captured scenes (>10,000 m2) often appears blurry and lacks detail. Merely increasing the model’s capacity or the number of sample points can significantly raise training costs. Existing space contraction methods, designed for forward-facing trajectory or the 360° object-centric trajectory, are not suitable for the unique trajectories of drone footage. Furthermore, anomalies and cloud fog artifacts, resulting from complex lighting conditions and sparse data acquisition, can significantly degrade the quality of rendering. To address these challenges, we propose a framework specifically designed for drone-captured scenes. Within this framework, while using a feature grid and multi-layer perceptron (MLP) to jointly represent 3D scenes, we introduce a Space Boundary Compression method and a Ground-Optimized Sampling strategy to streamline spatial structure and enhance sampling performance. Moreover, we propose an anti-aliasing neural rendering model based on Cluster Sampling and Integrated Hash Encoding to optimize distant details and incorporate an L1 norm penalty for outliers, as well as entropy regularization loss to reduce fluffy artifacts. To verify the effectiveness of the algorithm, experiments were conducted on four drone-captured scenes. The results show that, with only a single GPU and less than two hours of training time, photorealistic visualization can be achieved, significantly improving upon the performance of the existing NeRF approaches.

Elastic Seismic Imaging Enhancement of Sparse 4C Ocean-Bottom Node Data Using Deep Learning

The ocean bottom node (OBN) seismic acquisition system is designed to gather high-fidelity, wide-azimuth, and long-offset four-component (4C) data, which includes shear waves and enables the use of the elastic assumption in imaging and inversion. However, deploying geophysical instruments on the seafloor is difficult and costly, leading to the usual adoption of sparse node spacing. This can, however, lead to poor illumination and imaging challenges, especially in the shallow subsurface near the seafloor. To address these issues in the context of 4C elastic imaging, we propose a deep learning-based method using a multi-scale convolutional neural network (Ms-CNN) to improve the imaging quality of OBN surveys with sparse data acquisition. As an alternative to interpolating the sparse seismic data in the data domain, which can be a challenging task due to the limitations attributed to sampling theorem and the often larger amounts of data compared to the image, we train an Ms-CNN in a supervised fashion to map from sparse data images of PP and PS sections produced by 4C Gaussian beam migration to the equivalent dense data images, allowing for the direct processing of sparse data to improve imaging quality. Here, we combine the mean absolute error and multiscale structure similarity index measure in the loss function to optimize the network’s training process, and to help improve the performance. The effectiveness of the method is demonstrated through experiments on synthetic and field data, resulting in improved event continuity and reduced noise in migration results from sparse OBN acquisitions.

3D reflection seismic imaging of the Zinkgruvan mineral‐bearing structures in the south‐eastern Bergslagen mineral district (Sweden)

AbstractMineral exploration is facing greater challenges nowadays because of the increasing demand for raw materials and the lesser chance of finding large deposits at shallow depths. To be efficient and address new exploration challenges, high‐resolution and sensitive methods that are cost‐effective and environmentally friendly are required. In this work, we present the results of a sparse 3D seismic survey that was conducted in the Zinkgruvan mining area, in the Bergslagen mineral district of central Sweden. The survey covers an area of 10.5 km2 for deep targeting of massive sulphides in a polyphasic tectonic setting. A total of 1311 receivers and 950 shot points in a fixed 3D geometry setup were employed for the survey. Nine 2D profiles and a smaller 3D mesh were used. Shots were generated at every 10 m, and receivers were placed at every 10–20 m, along the 2D profiles, and 40–80 m in the mesh area. An analysis of the seismic fold coverage at depth was used to determine the potential resolving power of this sparse 3D setup. The data processing had to account for cultural noise from the operating mine and strong source‐generated surface waves, which were attenuated during both pre‐ and post‐stack processing steps. The processing workflow employed a combination of 2D and 3D refraction static corrections, and post‐stack FK filters along inlines and crosslines. The resulting 3D seismic volume is correlated with downhole data (density and P‐wave, acoustic impedance, reflection coefficient), synthetic seismograms, surface geology and a 3D model of mineral‐bearing horizons in order to suggest new exploration targets at depth. The overall geological architecture at Zinkgruvan is interpreted as two EW overturn folds, an antiform and a synform, affected by later NS‐trending folding. Two strong sets of shallow reflections, associated with the Zn–Pb mineralization, are located at the hinge of an EW‐trending antiform, while a strong set of reflections, associated with the main mineralization, is located at the overturned apex of the EW synform. The NS Knalla fault that crosses the study area terminates the continuation of the mineral‐bearing deposits at depth towards the west, a conclusion solely based on the reflectivity character of the seismic volume. This study illustrates that sparse 3D data acquisition, while it has its own challenges, can be a suitable replacement for 2D profiles while line cutting, and environmental footprints can totally be avoided.

Suppressing migration image artifacts using a support vector machine method

Reverse time migration (RTM) can produce high-quality images of complex subsurface structures when using seismic data acquired by a reasonably dense data acquisition geometry. However, RTM produces significant image artifacts when using data from a sparse data acquisition geometry because of incomplete cancellation of migration “smiles.” These artifacts obscure migration images of actual geology, leading to possible misidentification of important geologic features of interest. A specularity filter based on the semblance equation is commonly used in the dip-angle angle-domain common image gather (ADCIG) to preserve signals while suppressing image artifacts. In dip-angle ADCIG, the signals are assumed to have higher semblance scores because they are horizontally more coherent than the artifacts. However, this assumption fails when the image artifacts are severe. We have developed a new approach to suppressing migration image artifacts using a support vector machine (SVM) method. We first develop multiple criteria to distinguish between the signals and artifacts in the dip-angle ADCIG, rather than using only the semblance criterion. We then calculate the weights using a supervised SVM method. The weights approach one for valid signal points, and approach zero for artifact points. Finally, we apply the weights to the dip-angle ADCIG to preserve the effective signals and suppress the image artifacts. We verify the effectiveness of our method, denoted as SVM filtering, using numerical tests on synthetic and field data to produce migration images with improved signal-to-noise ratios and reduced aliasing artifacts.

Sparse Scanning Electron Microscopy Data Acquisition and Deep Neural Networks for Automated Segmentation in Connectomics.

With the growing importance of three-dimensional and very large field of view imaging, acquisition time becomes a serious bottleneck. Additionally, dose reduction is of importance when imaging material like biological tissue that is sensitive to electron radiation. Random sparse scanning can be used in the combination with image reconstruction techniques to reduce the acquisition time or electron dose in scanning electron microscopy. In this study, we demonstrate a workflow that includes data acquisition on a scanning electron microscope, followed by a sparse image reconstruction based on compressive sensing or alternatively using neural networks. Neuron structures are automatically segmented from the reconstructed images using deep learning techniques. We show that the average dwell time per pixel can be reduced by a factor of 2-3, thereby providing a real-life confirmation of previous results on simulated data in one of the key segmentation applications in connectomics and thus demonstrating the feasibility and benefit of random sparse scanning techniques for a specific real-world scenario.

Real-time three-dimensional MRI for the assessment of dynamic carpal instability.

BackgroundCarpal instability is defined as a condition where wrist motion and/or loading creates mechanical dysfunction, resulting in weakness, pain and decreased function. When conventional methods do not identify the instability patterns, yet clinical signs of instability exist, the diagnosis of dynamic instability is often suggested to describe carpal derangement manifested only during the wrist’s active motion or stress. We addressed the question: can advanced MRI techniques provide quantitative means to evaluate dynamic carpal instability and supplement standard static MRI acquisition? Our objectives were to (i) develop a real-time, three-dimensional MRI method to image the carpal joints during their active, uninterrupted motion; and (ii) demonstrate feasibility of the method for assessing metrics relevant to dynamic carpal instability, thus overcoming limitations of standard MRI.MethodsTwenty wrists (bilateral wrists of ten healthy participants) were scanned during radial-ulnar deviation and clenched-fist maneuvers. Images resulting from two real-time MRI pulse sequences, four sparse data-acquisition schemes, and three constrained image reconstruction techniques were compared. Image quality was assessed via blinded scoring by three radiologists and quantitative imaging metrics.ResultsReal-time MRI data-acquisition employing sparse radial sampling with a gradient-recalled-echo acquisition and constrained iterative reconstruction appeared to provide a practical tradeoff between imaging speed (temporal resolution up to 135 ms per slice) and image quality. The method effectively reduced streaking artifacts arising from data undersampling and enabled the derivation of quantitative measures pertinent to evaluating dynamic carpal instability.ConclusionThis study demonstrates that real-time, three-dimensional MRI of the moving wrist is feasible and may be useful for the evaluation of dynamic carpal instability.

Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices

One of the key issues in the acquisition of sparse data by means of compressed sensing is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the required number of measurements for sparse recovery. In this paper, we provide a new approach for the analysis of the restricted isometry constant (RIC) of finite dimensional Gaussian measurement matrices. The proposed method relies on the exact distributions of the extreme eigenvalues for Wishart matrices. First, we derive the probability that the restricted isometry property is satisfied for a given sufficient recovery condition on the RIC, and propose a probabilistic framework to study both the symmetric and asymmetric RICs. Then, we analyze the recovery of compressible signals in noise through the statistical characterization of stability and robustness. The presented framework determines limits on various sparse recovery algorithms for finite size problems. In particular, it provides a tight lower bound on the maximum sparsity order of the acquired data allowing signal recovery with a given target probability. Also, we derive simple approximations for the RICs based on the Tracy-Widom distribution.

Optical coherence elastography for strain dynamics measurements in laser correction of cornea shape.

We describe the use of elastographic processing in phase-sensitive optical coherence tomography (OCT) for visualizing dynamics of strain and tissue-shape changes during laser-induced photothermal corneal reshaping, for applications in the emerging field of non-destructive and non-ablative (non-LASIK) laser vision correction. The proposed phase-processing approach based on fairly sparse data acquisition enabled rapid data processing and near-real-time visualization of dynamic strains. The approach avoids conventional phase unwrapping, yet allows for mapping strains even for significantly supra-wavelength inter-frame displacements of scatterers accompanied by multiple phase-wrapping. These developments bode well for real-time feedback systems for controlling the dynamics of corneal deformation with 10-100 ms temporal resolution, and for suitably long-term monitoring of resultant reshaping of the cornea. In ex-vivo experiments with excised rabbit eyes, we demonstrate temporal plastification of cornea that allows shape changes relevant for vision-correction applications without affecting its transparency. We demonstrate OCT's ability to detect achieving of threshold temperatures required for tissue plastification and simultaneously characterize transient and cumulative strain distributions, surface displacements, and scattering tissue properties. Comparison with previously used methods for studying laser-induced reshaping of cartilaginous tissues and numerical simulations is performed.

Improving recovery of ECG signal with deterministic guarantees using split signal for multiple supports of matching pursuit (SS-MSMP) algorithm

Compressed sensing (CS) is a new field used for signal acquisition and design of sensor that made a large drooping in the cost of acquiring sparse signals. In this paper, new algorithms are developed to improve the performance of the greedy algorithms.In this paper, a new greedy pursuit algorithm, SS-MSMP (Split Signal for Multiple Support of Matching Pursuit), is introduced and theoretical analyses are given. The SS-MSMP is suggested for sparse data acquisition, in order to reconstruct analog and efficient signals via a small set of general measurements. This paper proposes a new fast method which depends on a study of the behavior of the support indices through picking the best estimation of the corrosion between residual and measurement matrix.The term multiple supports originates from an algorithm; in each iteration, the best support indices are picked based on maximum quality created by discovering correlation for a particular length of support.We depend on this new algorithm upon our previous derivative of halting condition that we produce for Least Support Orthogonal Matching Pursuit (LS-OMP) for clear and noisy signal.For better reconstructed results, SS-MSMP algorithm provides the recovery of support set for long signals such as signals used in WBAN.Numerical experiments demonstrate that the new suggested algorithm performs well compared to existing algorithms in terms of many factors used for reconstruction performance.

Influence of Error in Estimating Anisotropy Parameters on VTI Depth Imaging

Thin layers in sedimentary rocks lead to seismic anisotropy which makes the wave velocity dependent on the propagation angle. This aspect causes errors in seismic imaging such as mispositioning of migrated events if anisotropy is not accounted for. One of the challenging issues in seismic imaging is the estimation of anisotropy parameters which usually has error due to dependency on several elements such as sparse data acquisition and erroneous data with low signal-to-noise ratio. In this study, an isotropic and anelliptic VTI fast marching eikonal solvers are employed to obtain seismic travel times required for Kirchhoff depth migration algorithm. The algorithm solely uses compressional wave. Another objective is to study the influence of anisotropic errors on the imaging. Comparing the isotropic and VTI travel times demonstrates a considerable lateral difference of wavefronts. After Kirchhoff imaging with true anisotropy, as a reference, and with a model including error, results show that the VTI algorithm with error in anisotropic models produces images with minor mispositioning which is considerable for isotropic one specifically in deeper parts. Furthermore, over- or underestimating anisotropy parameters up to 30 percent are acceptable for imaging and beyond that cause considerable mispositioning.

Ultra-low dose CT attenuation correction for PET/CT: analysis of sparse view data acquisition and reconstruction algorithms

For PET/CT systems, PET image reconstruction requires corresponding CT images for anatomical localization and attenuation correction. In the case of PET respiratory gating, multiple gated CT scans can offer phase-matched attenuation and motion correction, at the expense of increased radiation dose. We aim to minimize the dose of the CT scan, while preserving adequate image quality for the purpose of PET attenuation correction by introducing sparse view CT data acquisition.We investigated sparse view CT acquisition protocols resulting in ultra-low dose CT scans designed for PET attenuation correction. We analyzed the tradeoffs between the number of views and the integrated tube current per view for a given dose using CT and PET simulations of a 3D NCAT phantom with lesions inserted into liver and lung. We simulated seven CT acquisition protocols with {984, 328, 123, 41, 24, 12, 8} views per rotation at a gantry speed of 0.35 s. One standard dose and four ultra-low dose levels, namely, 0.35 mAs, 0.175 mAs, 0.0875 mAs, and 0.043 75 mAs, were investigated. Both the analytical Feldkamp, Davis and Kress (FDK) algorithm and the Model Based Iterative Reconstruction (MBIR) algorithm were used for CT image reconstruction. We also evaluated the impact of sinogram interpolation to estimate the missing projection measurements due to sparse view data acquisition. For MBIR, we used a penalized weighted least squares (PWLS) cost function with an approximate total-variation (TV) regularizing penalty function. We compared a tube pulsing mode and a continuous exposure mode for sparse view data acquisition. Global PET ensemble root-mean-squares-error (RMSE) and local ensemble lesion activity error were used as quantitative evaluation metrics for PET image quality.With sparse view sampling, it is possible to greatly reduce the CT scan dose when it is primarily used for PET attenuation correction with little or no measureable effect on the PET image. For the four ultra-low dose levels simulated, sparse view protocols with 41 and 24 views best balanced the tradeoff between electronic noise and aliasing artifacts. In terms of lesion activity error and ensemble RMSE of the PET images, these two protocols, when combined with MBIR, are able to provide results that are comparable to the baseline full dose CT scan. View interpolation significantly improves the performance of FDK reconstruction but was not necessary for MBIR. With the more technically feasible continuous exposure data acquisition, the CT images show an increase in azimuthal blur compared to tube pulsing. However, this blurring generally does not have a measureable impact on PET reconstructed images.Our simulations demonstrated that ultra-low-dose CT-based attenuation correction can be achieved at dose levels on the order of 0.044 mAs with little impact on PET image quality. Highly sparse 41- or 24- view ultra-low dose CT scans are feasible for PET attenuation correction, providing the best tradeoff between electronic noise and view aliasing artifacts. The continuous exposure acquisition mode could potentially be implemented in current commercially available scanners, thus enabling sparse view data acquisition without requiring x-ray tubes capable of operating in a pulsing mode.

Correction of Reflectance Anisotropy Effects of Vegetation on Airborne Spectroscopy Data and Derived Products

Directional effects in airborne imaging spectrometer (IS) data are mainly caused by anisotropic reflectance behavior of surfaces, commonly described by bi-directional reflectance distribution functions (BRDF). The radiometric and spectral accuracy of IS data is known to be highly influenced by such effects, which prevents consistent comparison of products. Several models were developed to approximate surface reflectance anisotropy for multi-angular observations. Few studies were carried out using such models for airborne flight lines where only a single observation is available for each ground location. In the present work, we quantified and corrected reflectance anisotropy on a single airborne HyMap flight line using a Ross-Li model. We stratified the surface in two vegetation structural types (different in vertical structuring) using spectral angle mapping, to generate a structure dependent set of angular observations. We then derived a suite of products [indices (structure insensitive pigment index, normalized difference vegetation index, simple ratio index, and anthocyanin reflectance index) and inversion-based (SAIL/PROSPECT-leaf area index, Cw, Cdm, Cab)] from corrected and uncorrected images. Non-parametric analysis of variance (Kruskal-Wallis test) showed throughout significant improvements in products from corrected images. Data correction resulting in airborne nadir BRDF adjusted reflectance (aNBAR) showed uncertainty reductions from 60 to 100% (p-value = 0.05) as compared to uncorrected and nadir observations. Using sparse IS data acquisitions, the use of fully parametrized BRDF models is limited. Our normalization scheme is straightforward and can be applied with illumination and observation geometry being the only a priori information. We recommend aNBAR generation to precede any higher level airborne IS product generation based on reflectance data.

Fast method of sparse acquisition and reconstruction of view and illumination dependent datasets

Although computer graphics uses measured view and illumination dependent data to achieve realistic digital reproduction of real-world material properties, the extent of their utilization is currently limited by a complicated acquisition process. Due to the high dimensionality of such data, the acquisition process is demanding on time and resources. Proposed is a method of approximate reconstruction of the data from a very sparse dataset, obtained quickly using inexpensive hardware. This method does not impose any restrictions on input datasets and can handle anisotropic, non-reciprocal view and illumination direction-dependent data. The method's performance was tested on a number of isotropic and anisotropic apparent BRDFs, and the results were encouraging. The method performs better than the uniform sampling of a comparable sample count and has three main benefits: the sparse data acquisition can be done quickly using inexpensive hardware, the measured material does not need to be extracted or removed from its environment, and the entire process of data reconstruction from the sparse samples is quick and reliable. Finally, the ease of sparse dataset acquisition was verified in measurement experiments with three materials, using a simple setup of a consumer camera and a single LED light. The proposed method has also shown promising performance when applied to sparse measurement and reconstruction of BTFs, mainly for samples with a lower surface height variation. Our approach demonstrates solid performance across a wide range of view and illumination dependent datasets, therefore creating a new opportunity for development of time and cost-effective portable acquisition setups.

Design and Analysis of a Hardware-Efficient Compressed Sensing Architecture for Data Compression in Wireless Sensors

This work introduces the use of compressed sensing (CS) algorithms for data compression in wireless sensors to address the energy and telemetry bandwidth constraints common to wireless sensor nodes. Circuit models of both analog and digital implementations of the CS system are presented that enable analysis of the power/performance costs associated with the design space for any potential CS application, including analog-to-information converters (AIC). Results of the analysis show that a digital implementation is significantly more energy-efficient for the wireless sensor space where signals require high gain and medium to high resolutions. The resulting circuit architecture is implemented in a 90 nm CMOS process. Measured power results correlate well with the circuit models, and the test system demonstrates continuous, on-the-fly data processing, resulting in more than an order of magnitude compression for electroencephalography (EEG) signals while consuming only 1.9 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu$</tex></formula> W at 0.6 V for sub-20 kS/s sampling rates. The design and measurement of the proposed architecture is presented in the context of medical sensors, however the tools and insights are generally applicable to any sparse data acquisition.

Structured sublinear compressive sensing via belief propagation

Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design of structured sensing matrices and logarithmic-complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with orthogonal matching pursuit (OMP) methods. For reduced-complexity greedy reconstruction schemes, we propose a new family of list-decoding belief propagation algorithms, as well as reinforced and multiple-basis belief propagation (BP) algorithms. Our simulation results indicate that reinforced BP CS schemes offer very good complexity–performance tradeoffs for very sparse signal vectors.

WE‐A‐301‐07: Using Prior Images with Registration in Penalized Likelihood Estimation for CT with Sparse Data

Purpose: We aim to develop tomographic reconstruction methods that utilize prior CT volumes to improve image quality for sparse and undersampled datasets. The ability to handle such data has applications in region‐of‐interest scanning, tomosynthesis, and intraoperative imaging based on few view angles. While compressed sensing techniques like the PICCS algorithm are attractive, there are potential drawbacks. Such approaches often rely on pre‐registered prior images and the forward models for PICCS‐type algorithms tend to be simplified and ignore the noise model. We leverage the ability of likelihood‐based techniques to incorporate both prior images and sophisticated forward models. Methods: We have developed a framework for reconstruction of sparse tomographic data based on penalized‐likelihood estimation. The objective function for this approach is composed of a likelihood term that incorporates the forward model and noise; and a parameterized penalty term that discourages differences from the prior image. The penalty uses a compressed sensing norm and is parameterized to accommodate registration of the prior scan. An iterative algorithm is used to simultaneously solve for the tomographic volume and the registration parameters. The framework is general and can be used with both rigid and deformable registrations. Results: Reconstruction of sparse data using the proposed approach is demonstrated in cases where either rigid or deformable registration is employed in the reconstruction objective. We compare reconstruction results with traditional approaches where prior image data is not utilized. We find a substantial improvement in image quality with significant reduction in artifacts that are associated with the sparse data acquisitions. Conclusions: A new class of penalized‐likelihood estimator has been developed that simultaneously refines attenuation and registration estimates. The framework is general and supports both rigid and non‐rigid transformations of the prior imagery. Image quality and handling of artifacts using the proposed estimator with sparse data is superior to traditional approaches.

Estimation of spatial–temporal rainfall distribution using remote sensing techniques: A case study of Makanya catchment, Tanzania

Rainfall–runoff modeling provides an opportunity to easily simulate the response of a watershed, thus providing an option for sustainable water resources management particularly in dry regions of Sub-Saharan Africa (SSA). Analysis of rainfall–runoff relationships in a catchment forms the basis of hydrological modeling. However, rainfall is a highly dynamic process, constantly changing in form and intensity as it passes over a given area. Traditionally, rainfall is measured using limited rain gauges at ground stations and often, the dynamics are not captured and yet it is the main input variable in any hydrological modeling. Without improved rainfall estimation, flow discharge estimates from rainfall–runoff relationship in both gauged and ungauged catchments particularly in arid and semi-arid regions remain a major challenge.Application of remote sensing information becomes crucial in the process of estimating rainfall patterns of these areas. The estimation of rainfall in this study was based on the blending of the geostationary MeteoSat Second Generation (MSG), infrared channel with the low-earth orbiting passive Tropical Rainfall Measuring Mission (TRMM), and microwave channel satellite data. To combine these two satellite data, a regression function associated with a threshold as an upper cloud temperature limit where rain occurs was determined. In this way, Makanya catchment rainfall maps (daily, monthly, and seasonal) with 3km pixel size from 2004 to 2006 were generated by aggregating the 15min rainfall values. Comparison of the results obtained from the blended TRMM–MSG with the available ground gauge data for 2004 and 2005 periods, gave a good correlation of about 80%. In conclusion, the developed TRMM–MSG blending procedure was found to be a reliable and robust way of obtaining spatial–temporal rainfall distribution of a given area and particularly so for arid and semi-arid lands (ASALs) such as Makanya with sparse data acquisition networks.