Scatter Estimation Research Articles

Machine Learning in PET: from Photon Detection to Quantitative Image Reconstruction.

Machine learning has found unique applications in nuclear medicine from photon detection to quantitative image reconstruction. While there have been impressive strides in detector development for time-of-flight positron emission tomography, most detectors still make use of simple signal processing methods to extract the time and position information from the detector signals. Now with the availability of fast waveform digitizers, machine learning techniques have been applied to estimate the position and arrival time of high-energy photons. In quantitative image reconstruction, machine learning has been used to estimate various corrections factors, including scattered events and attenuation images, as well as to reduce statistical noise in reconstructed images. Here machine learning either provides a faster alternative to an existing time-consuming computation, such as in the case of scatter estimation, or creates a data-driven approach to map an implicitly defined function, such as in the case of estimating the attenuation map for PET/MR scans. In this article, we will review the abovementioned applications of machine learning in nuclear medicine.

Geosynchronous SAR Tomography: Theory and First Experimental Verification Using Beidou IGSO Satellite

Synthetic aperture radar (SAR) tomography (TomoSAR) techniques exploit multipass acquisitions of the same scene with slightly different view angles, and allow generating fully 3-D images, providing an estimation of scatterers’ distribution along range, azimuth, and elevation directions. This paper extends TomoSAR to geosynchronous SAR (GEO TomoSAR). First, the potential and performance of GEO TomoSAR were analyzed from the perspective of orbital perturbation and the resulting large spatial baseline. Then, the rotation-induced decorrelation problems induced by the along-track baseline component were analyzed. In addition, the optimized acquisition geometry and tomographic processing flow were given, and the computer simulation verification was also completed. Finally, the equivalent validation experiment based on Beidou inclined geosynchronous orbit (IGSO) navigation satellite was carried out to demonstrate the feasibility and effectiveness of GEO TomoSAR. The experimental system employs the Beidou IGSO satellite as illuminator of opportunity and a ground system collecting and processing reflected echoes. This is the first time to employ the data from repeat-track Beidou IGSO satellites for tomographic processing. The 3-D imaging of the urban area using this experimental system was presented and then verified using LiDAR cloud data as reference. The results show that GEO TomoSAR can form the baseline of the order of hundreds of kilometers in elevation, which has the ability to achieve a resolution of 5 m in elevation.

Ultrasound simulation with deformable and patient-specific scatterer maps.

Ray-tracing-based simulations model ultrasound (US) interactions with a custom geometric anatomical model, where US texture can be emulated via real-time point-spread function convolutions of a tissue scatterer representation. Such scatterer representations for realistic appearance are difficult to parameterize or model manually and do not respond to volumetric deformations such as those caused with tissue compression by the probe. Herein we utilize brightness mode (B-mode) estimated scatterer maps for ray tracing and propose to enhance the realism of ray-tracing-based simulations by incorporating dynamic speckle patterns that change compliant with tissue deformation. In this work, we realistically simulate US texture deformations in the scatterer domain via back-projection of ray segments into a nominal state before sampling during simulation runtime. We estimate scatterer maps from background in vivo images using a pretrained generative adversarial network. We demonstrated our proposed scatterer estimation and runtime background fusion method on simulated transvaginal US scans of detailed surface-based foetal models. We show the viability of modelling deformations in the scatterer domain at interactive frame rates of 28 frames per second. A quantitative and a qualitative evaluations indicated improved realism in comparison to the state of the art. Transferring a background image in a scatterer representation enables us to capture anatomical content in a physical space, in which deformations can be incorporated physically consistently before convolving with a US point-spread function during simulation runtime. This then uses the same imaging model on both the background and the hand-crafted models leading to a consistent and seamless compounding of contents in the scatterer space.

Enabling machine learning in X-ray-based procedures via realistic simulation of image formation.

Machine learning-based approaches now outperform competing methods in most disciplines relevant to diagnostic radiology. Image-guided procedures, however, have not yet benefited substantially from the advent of deep learning, in particular because images for procedural guidance are not archived and thus unavailable for learning, and even if they were available, annotations would be a severe challenge due to the vast amounts of data. In silico simulation of X-ray images from 3D CT is an interesting alternative to using true clinical radiographs since labeling is comparably easy and potentially readily available. We extend our framework for fast and realistic simulation of fluoroscopy from high-resolution CT, called DeepDRR, with tool modeling capabilities. The framework is publicly available, open source, and tightly integrated with the software platforms native to deep learning, i.e.,Python, PyTorch, and PyCuda. DeepDRR relies on machine learning for material decomposition and scatter estimation in 3D and 2D, respectively, but uses analytic forward projection and noise injection to ensure acceptable computation times. On two X-ray image analysis tasks, namely (1) anatomical landmark detection and (2) segmentation and localization of robot end-effectors, we demonstrate that convolutional neural networks (ConvNets) trained on DeepDRRs generalize well to real data without re-training or domain adaptation. To this end, we use the exact same training protocol to train ConvNets on naïve and DeepDRRs and compare their performance on data of cadaveric specimens acquired using a clinical C-arm X-ray system. Our findings are consistent across both considered tasks. All ConvNets performed similarly well when evaluated on the respective synthetic testing set. However, when applied to real radiographs of cadaveric anatomy, ConvNets trained on DeepDRRs significantly outperformed ConvNets trained on naïve DRRs ([Formula: see text]). Our findings for both tasks are positive and promising. Combined with complementary approaches, such as image style transfer, the proposed framework for fast and realistic simulation of fluoroscopy from CT contributes to promoting the implementation of machine learning in X-ray-guided procedures. This paradigm shift has the potential to revolutionize intra-operative image analysis to simplify surgical workflows.

Stochastic modelling of star-formation histories I: the scatter of the star-forming main sequence

ABSTRACT We present a framework for modelling the star-formation histories of galaxies as a stochastic process. We define this stochastic process through a power spectrum density with a functional form of a broken power law. Star-formation histories are correlated on short time-scales, the strength of this correlation described by a power-law slope, α, and they decorrelate to resemble white noise over a time-scale that is proportional to the time-scale of the break in the power spectrum density, τbreak. We use this framework to explore the properties of the stochastic process that, we assume, gives rise to the log-normal scatter about the relationship between star-formation rate and stellar mass, the so-called galaxy star-forming main sequence. Specifically, we show how the measurements of the normalization and width (σMS) of the main sequence, measured in several passbands that probe different time-scales, give a constraint on the parameters of the underlying power spectrum density. We first derive these results analytically for a simplified case where we model observations by averaging over the recent star-formation history. We then run numerical simulations to find results for more realistic observational cases. As a proof of concept, we use observational estimates of the main sequence scatter at z ∼ 0 and M⋆ ≈ 1010 M⊙ measured in H α, UV+IR, and the u-band. The result is degenerate in the τbreak-α space, but if we assume α = 2, we measure $\tau _{\rm break}=170^{+169}_{-85}~\mathrm{Myr}$. This implies that star-formation histories of galaxies lose ‘memory’ of their previous activity on a time-scale of ∼200 Myr.

Common multivariate estimators of location and scatter capture the symmetry of the underlying distribution

The article discusses how various multivariate location and scatter estimators capture the symmetry of the underlying distribution. Very general sufficient conditions are formulated, which ensure various symmetry properties of functionals corresponding to location or scatter. Examples of robust multivariate estimators, which fulfill these conditions, are discussed in detail. The obtained symmetry of the estimators is applicable to hypothesis tests of symmetry of the underlying distribution of the multivariate data. For this task, we propose to perform permutation tests exploiting the nonparametric combination methodology. The performance of the newly proposed tests is illustrated on simulated as well as real data. The tests are suitable for small sample sizes and represent the first available symmetry tests suitable also for non-elliptical distributions and for more than just two variables.

Quantitative Cone-Beam CT of Bone Mineral Density Using Model-Based Reconstruction.

We develop and validate a model-based framework for artifact correction and image reconstruction to enable application of Cone-Beam CT (CBCT) in quantitative assessment of bone mineral density (BMD). Compared to conventional quantitative CT, this approach does not require a BMD calibration phantom in the field-of-view during an object scan. The quantitative CBCT (qCBCT) imaging framework combined fast Monte Carlo (MC) scatter estimation, accurate models of detector response, and polyenergetic Poisson likelihood (PolyPL, Elbakri et al 2003). The underlying object model assumed that the tissues were ideal mixtures of water and calcium carbonate (CaCO3). Accuracy and reproducibility of qCBCT was evaluated in benchtop test-retest studies emulating a compact extremity CBCT system (axis-detector distance=56 cm, 90 kVp x-ray beam, ~16 mGy central dose). Various arrangements of Ca inserts (50-500 mg/mL) were placed in water cylinders of ~11 cm to ~15 cm diameter and scanned at multiple positions inside the field-of-view for a total of 20 configurations. In addition, a cadaveric ankle was imaged in five configurations (with and without Ca inserts and water bath). Coefficient of variation (CV) of BMD values across different experimental configurations was used to assess reproducibility under varying imaging conditions. The performance of the model-based qCBCT framework (MC + PolyPL) was compared to FDK with water beam hardening correction and MC scatter correction. The PolyPL framework achieved accuracy of 20 mg/mL or better across all insert densities and experimental configurations. By comparison, the accuracy of the FDK-based BMD estimates deteriorated with higher mineralization, resulting in ~120 mg/mL error for a 500 mg/mL Ca insert. Additionally, the model-based approach mitigated residual streaks that were present in FDK reconstructions. The CV of both methods was ~15% at 50 mg/mL Ca and less than ~8% for higher density inserts, where the PolyPL framework achieved 20-25% lower CV than the FDK-based approach. Accurate and reproducible BMD measurements can be achieved in extremity CBCT, supporting clinical applications in quantitative monitoring of fracture risk, osteoporosis treatment, and early osteoarthritis.

Intrinsic Cramér–Rao Bounds for Scatter and Shape Matrices Estimation in CES Distributions

Scatter matrix and its normalized counterpart, referred to as shape matrix, are key parameters in multivariate statistical signal processing, as they generalize the concept of covariance matrix in the widely used Complex Elliptically Symmetric distributions. Following the framework of [1], intrinsic Cramér-Rao bounds are derived for the problem of scatter and shape matrices estimation with samples following a Complex Elliptically Symmetric distribution. The Fisher Information Metric and its associated Riemannian distance (namely, CES-Fisher) on the manifold of Hermitian positive definite matrices are derived. Based on these results, intrinsic Cramér-Rao bounds on the considered problems are then expressed for three different distances (Euclidean, natural Riemannian, and CES-Fisher). These contributions are therefore a generalization of Theorems 4 and 5 of [1] to a wider class of distributions and metrics for both scatter and shape matrices.

A Data-Cleaning Approach to Robust Multisensor Detection of Improper Signals

We consider the problem of detecting the presence of an improper complex-valued signal, common among two or more sensors (channels), in the presence of spatially independent, colored improper noise and additive outliers. A source of improper noise is in-phase/quadrature-phase imbalance during down-conversion of bandpass noise to baseband at the receiver. For clean data (i.e., known to be outlier free), a nonparametric binary hypothesis testing formulation in frequency-domain, utilizing the discrete Fourier transform of an augmented measurement sequence, has been proposed in the literature, and it results in a generalized likelihood ratio test (GLRT). In this paper we robustify this approach against additive outliers in the data, using a data-cleaning approach. Using some existing robust estimators of multivariate scatter, we first detect the outliers, and subsequently remove and replace them using vector median filtering to yield cleaned data. The existing GLRT is then applied to the cleaned data. The approach is illustrated via simulations. The considered problem has applications in diverse areas including spectrum sensing for cognitive radio.

Robust Spectrum-Based Comparison of Multivariate Complex Random Signals

We consider the problem of comparing two complex multivariate random signal realizations, possibly contaminated with additive outliers, to ascertain whether they have identical power spectral densities. For clean data (i.e., known to be outlier free), a binary hypothesis testing formulation in frequency-domain, utilizing the estimated power spectral density matrices, has been proposed in the literature, and it results in a generalized likelihood ratio test (GLRT). In this paper, we first present an alternative, principled derivation of the existing GLRT using the asymptotic distribution of a frequency-domain sufficient statistic, based on the discrete Fourier transform of the two signal realizations. In order to robustify this GLRT in the presence of additive outliers, we first exploit an existing robust estimator of multivariate scatter to detect the outliers, and subsequently, to clean the data. The existing GLRT is then applied to the cleaned signal realizations. The approach is illustrated through simulations. The considered problem has applications in diverse areas, including user authentication in wireless networks with multi-antenna receivers.

Real-time scatter estimation for medical CT using the deep scatter estimation: Method and robustness analysis with respect to different anatomies, dose levels, tube voltages, and data truncation.

X-ray scattering leads to CT images with a reduced contrast, inaccurate CT values as well as streak and cupping artifacts. Therefore, scatter correction is crucial to maintain the diagnostic value of CT and CBCT examinations. However, existing approaches are not able to combine both high accuracy and high computational performance. Therefore, we propose the deep scatter estimation (DSE): a deep convolutional neural network to derive highly accurate scatter estimates in real time. Gold standard scatter estimation approaches rely on dedicated Monte Carlo (MC) photon transport codes. However, being computationally expensive, MC methods cannot be used routinely. To enable real-time scatter correction with similar accuracy, DSE uses a deep convolutional neural network that is trained to predict MC scatter estimates based on the acquired projection data. Here, the potential of DSE is demonstrated using simulations of CBCT head, thorax, and abdomen scans as well as measurements at an experimental table-top CBCT. Two conventional computationally efficient scatter estimation approaches were implemented as reference: a kernel-based scatter estimation (KSE) and the hybrid scatter estimation (HSE). The simulation study demonstrates that DSE generalizes well to varying tube voltages, varying noise levels as well as varying anatomical regions as long as they are appropriately represented within the training data. In any case the deviation of the scatter estimates from the ground truth MC scatter distribution is less than 1.8% while it is between 6.2% and 293.3% for HSE and between 11.2% and 20.5% for KSE. To evaluate the performance for real data, measurements of an anthropomorphic head phantom were performed. Errors were quantified by a comparison to a slit scan reconstruction. Here, the deviation is 278HU (no correction), 123HU (KSE), 65HU (HSE), and 6HU (DSE), respectively. The DSE clearly outperforms conventional scatter estimation approaches in terms of accuracy. DSE is nearly as accurate as Monte Carlo simulations but is superior in terms of speed (≈10ms/projection) by orders of magnitude.

A new software scheme for scatter correction based on a simple radiographic scattering model.

In common radiography, image contrast is often limited due mainly to scattered x-rays and noise, decreasing the quantitative usefulness of x-ray images. Several scatter reduction methods based on software correction schemes have been extensively investigated in an attempt to overcome these difficulties, most of which are based on measurement, mathematical-physical modeling, or a combination of both. However, those methods require special equipment, system geometry, and extra manual work to measure scatter characteristics. In this study, we investigated a new software scheme for scatter correction based on a simple radiographic scattering model where the intensity of the scattered x-rays was directly estimated from a single x-ray image using a weighted l1-norm contextual regularization framework. We implemented the proposed algorithm and performed a systematic simulation and experiment to demonstrate its viability. We also conducted some clinical image studies using patient's image data of breast and L-spine to verify the clinical effectiveness of the proposed scheme. Our results indicate that the degradation of image characteristics by scattered x-rays and noise was effectively recovered by using the proposed software scheme, thus improving radiographic visibility considerably. Graphical abstract The schematic illustrations of scatter suppression methods by using a an antiscatter grid and b a scatter estimation algorithm.

OA127] Cone-beam CT intensity correction for adaptive radiotherapy of the prostate using deep learning

Purpose This study investigates for the first time the feasibility of using deep learning for cone-beam CT (CBCT) intensity correction to enable accurate daily dose calculation and treatment adaptation in volumetric-modulated arc therapy (VMAT) and intensity-modulated proton therapy (IMPT). Current CBCT intensity correction approaches often show a lack of either speed or accuracy, which might be overcome by deep learning approaches. Methods Pre-treatment CBCTs and corresponding projections of 30 prostate cancer patients were considered. A previously validated technique for CBCT intensity correction, based on deformable image registration (DIR) of the planning CT to the daily CBCT and scatter estimation in projection space, served as reference (CBCTcor) [1] . Two alternative methods were investigated: A U-shaped deep convolutional neural network (U-Net) was trained to perform scatter correction in projection space, i.e., going from measured to corrected projections before reconstruction (CBCTScatterNet). Moreover, a generative adversarial network (GAN) was trained to perform a translation from the original CBCT (CBCTorg) to CBCTcor in image space, generating a so-called CBCTcorGAN. CBCTScatterNet and CBCTcorGAN were compared to CBCTcor in terms of mean absolute error (MAE) and mean error (ME). For eight exemplary patients, dose calculation accuracy in VMAT and IMPT was evaluated with respect to CBCTorg. Results Both, CBCTScatterNet and CBCTcorGAN, showed a substantially improved agreement to CBCTcor compared to CBCTorg. Mean MAE and ME decreased from 158HU and 152HU for CBCTorg to 39HU and 4HU for CBCTScatterNet and 57HU and −2HU for CBCTcorGAN, respectively. In a 2% dose-difference test, considering only voxels above 50% of the prescribed dose, mean pass-rates were 53% and 64% for CBCTScatterNet and CBCTcorGAN in IMPT. In VMAT, pass-rates of 90% and 97% were obtained for CBCTScatterNet and CBCTcorGAN using a 1% dose-difference criterion. Conclusions CBCT intensity correction using two different implementations of deep learning was found feasible. For VMAT, dose calculation accuracy was high, while for IMPT further improvements may be required. Compared to the reference correction method, deep learning techniques were less affected by DIR inaccuracies and allowed considerably faster CBCT correction within few seconds instead of minutes.

LCF behaviour and a comprehensive life prediction model for AlSi10Mg obtained by SLM

The full potential of additive manufacturing (AM) components is today yet to be reached. Space and aerospace industries are still conservative in the use of AM parts for safety–critical applications, mostly because of the uncertainties and low reproducibility that are often associated with the process. One of the most challenging issues is the fatigue resistance. The rough surface condition and the presence of manufacturing defects can cause significant scatter, leading to the adoption of large conservative safety factors. To robustly model the fatigue resistance of defected AM materials, there is a need to implement defect-tolerant designs and deal with these uncertainties. The present research activity aims at developing a model for fatigue life estimation in a large range of loading conditions, from high cycle fatigue to low cycle fatigue. This is achieved by adopting a fracture mechanics approach, through elastic–plastic fatigue crack growth calculations based on the known defect population inside the material. The model has been applied to AlSi10Mg produced by three slightly different selective laser melting processes, showing a robust estimation of fatigue life and scatter with limited experimental effort. The life predictions performed are then summarised in design maps where the allowable stress (or strain) depends on the defect size and on the HCF/LCF design upon the number of cycles selected.

Weighted likelihood estimation of multivariate location and scatter

A novel approach to obtain weighted likelihood estimates of multivariate location and scatter is discussed. A weighting scheme is proposed that is based on the univariate distribution of the Mahalanobis distances rather than the multivariate distribution of the data at the assumed model. This strategy allows to avoid the curse of dimensionality affecting multivariate non-parametric density estimation, that is involved in the construction of the weights through the Pearson residuals. Asymptotic properties of the proposed weighted likelihood estimator are also discussed. Then, weighted likelihood-based outlier detection rules and robust dimensionality reduction techniques are developed. The effectiveness of the methodology is illustrated through some numerical studies and real data examples.

Deep Scatter Estimation (DSE): Accurate Real-Time Scatter Estimation for X-Ray CT Using a Deep Convolutional Neural Network

X-ray scatter is a major cause of image quality degradation in dimensional CT. Especially, in case of highly attenuating components scatter-to-primary ratios may easily be higher than 1. The corresponding artifacts which appear as cupping or dark streaks in the CT reconstruction may impair a metrological assessment. Therefore, an appropriate scatter correction is crucial. Thereby, the gold standard is to predict the scatter distribution using a Monte Carlo (MC) code and subtract the corresponding scatter estimate from the measured raw data. MC, however, is too slow to be used routinely. To correct for scatter in real-time, we developed the deep scatter estimation (DSE). It uses a deep convolutional neural network which is trained to reproduce the output of MC simulations using only the acquired projection data as input. Once trained, DSE can be applied in real-time. The present study demonstrates the potential of the proposed approach using simulations and measurements. In both cases the DSE yields highly accurate scatter estimates that differ by< 3% from our MC scatter predictions. Further, DSE clearly outperforms kernel-based scatter estimation techniques and hybrid approaches, as they are in use today.

Effect of detruncation on the accuracy of Monte Carlo-based scatter estimation in truncated CBCT.

The purpose of this study is to investigate the necessity of detruncation for scatter estimation of truncated cone-beam CT (CBCT) data and to evaluate different detruncation algorithms. Scattered radiation results in some of the most severe artifacts in CT and depends strongly on the size and the shape of the scanned object. Especially in CBCT systems the large cone-angle and the small detector-to-isocenter distance lead to a large amount of scatter detected, resulting in cupping artifacts, streak artifacts, and inaccurate CT-values. If a small field of measurement (FOM) is used, as it is often the case in CBCT systems, data are truncated in longitudinal and lateral direction. Since only truncated data are available as input for the scatter estimation, the already challenging correction of scatter artifacts becomes even more difficult. The following detruncation methods are compared and evaluated with respect to scatter estimation: constant detruncation, cosine detruncation, adaptive detruncation, and prior-based detruncation using anatomical data from a similar phantom or patient, also compared to the case where no detruncation was performed. Each of the resulting, detruncated reconstructions serve as input volume for a Monte Carlo (MC) scatter estimation and subsequent scatter correction. An evaluation is performed on a head simulation, measurements of a head phantom and a patient using a dental CBCT geometry with a FOM diameter of 11cm. Additionally, a thorax phantom is measured to assess performance in a C-Arm geometry with a FOM of up to 20cm. If scatter estimation is based on simple detruncation algorithms like a constant or a cosine detruncation scatter is estimated inaccurately, resulting in incorrect CT-values as well as streak artifacts in the corrected volume. For the dental CBCT phantom measurement CT-values for soft tissue were corrected from -204HU (no scatter correction) to -87HU (no detruncation), -218HU (constant detruncation), -141HU (cosine detruncation), -91HU (adaptive detruncation), -34HU (prior-based detruncation using a different prior) and -24HU (prior-based detruncation using the identical prior) for a reference value of -26HU measured in slit scan mode. In all cases the prior-based detruncation results in the best scatter correction, followed by the adaptive detruncation, as these algorithms provide a rather accurate model of high-density structures outside the FOM, compared to a simple constant or a cosine detruncation. Our contribution is twofold: first we give a comprehensive comparison of various detruncation methods for the purpose of scatter estimation. We find that the choice of the detruncation method has a significant influence on the quality of MC-based scatter correction. Simple or no detruncation is often insufficient for artifact removal and results in inaccurate CT-values. On the contrary, prior-based detruncation can achieve a high CT-value accuracy and nearly artifact-free volumes from truncated CBCT data when combined with other state-of-the-art artifact corrections. Secondly, we show that prior-based detruncation is effective even with data from a different patient or phantom. The fact that data completion does not require data from the same patient dramatically increases the applicability and usability of this scatter estimation.

Clinical Evaluation of 68Ga-PSMA-II and 68Ga-RM2 PET Images Reconstructed With an Improved Scatter Correction Algorithm.

Gallium-68-labeled radiopharmaceuticals pose a challenge for scatter estimation because their targeted nature can produce high contrast in these regions of the kidneys and bladder. Even small errors in the scatter estimate can result in washout artifacts. Administration of diuretics can reduce these artifacts, but they may result in adverse events. Here, we investigated the ability of algorithmic modifications to mitigate washout artifacts and eliminate the need for diuretics or other interventions. The model-based scatter algorithm was modified to account for PET/MRI scanner geometry and challenges of non-FDG tracers. Fifty-three clinical 68Ga-RM2 and 68Ga-PSMA-11 whole-body images were reconstructed using the baseline scatter algorithm. For comparison, reconstruction was also processed with modified sampling in the single-scatter estimation and with an offset in the scatter tail-scaling process. None of the patients received furosemide to attempt to decrease the accumulation of radiopharmaceuticals in the bladder. The images were scored independently by three blinded reviewers using the 5-point Likert scale. The scatter algorithm improvements significantly decreased or completely eliminated the washout artifacts. When comparing the baseline and most improved algorithm, the image quality increased and image artifacts were reduced for both 68Ga-RM2 and for 68Ga-PSMA-11 in the kidneys and bladder regions. Image reconstruction with the improved scatter correction algorithm mitigated washout artifacts and recovered diagnostic image quality in 68Ga PET, indicating that the use of diuretics may be avoided.

Robust Monitoring of Industrial Processes in the Presence of Outliers in Training Data

Data-driven process monitoring methods often use classical multivariate statistical analysis (MSA) techniques for data analysis and modeling, with the assumption that the training data contains only observations associated with normal operating conditions of a process. In practice, the training data of an industrial process may contain outliers. Classical MSA methods can be affected by outliers so strongly that the resulting monitoring methods do not allow to detect true process faults. In this paper, a robust process monitoring method is proposed to cope with the presence of outliers in the training data. First, the minimum covariance determinant (MCD) estimator is used for outlier detection and to obtain the robust estimation of location and scatter of training data. A robust fault detection index, called the robust T2 statistic, is then defined based on the MCD estimator. Squared variable deviation magnitude (SVDM) is defined as a robust measure of the deviation of a process variable from the normal ra...

Estimation and Reduction of Resonant Mie Scattering (RMieS) From IR Spectra of Biological Cells by Optimization Algorithm

Infrared spectroscopy has attracted considerable attention at many fields of study such as pharmaceutical sciences. How much scattering we have would be based on the similarities range of mid-infrared wavelength and uneven biological samples like cells and tissues. In such cases, the part of the input irradiance wave which does not reach the detector could erroneously be interpreted as absorption intensity. So it shows itself as a broad sinusoidal oscillation in the baseline, and even it would have frequency shifts in the absorbance bands. Based on the studies conducted in this area, the main cause of spectral distortion is the Resonant Mie Scattering. In other words, the real refractive index spectrum plays a prominent role in high scattering. However, pure absorptive components extraction suffers from requiring an appropriate reference spectrum for initialization. It must not contain any scattering contributions which unfortunately cannot be always happened. In this article, a cost function under a clear constraint is presented with regard to the biological data and the scattering structure to spectrum correction. The results show that the creation of eligible cost function using optimization algorithms could have the desired accuracy for biological spectra even without selecting appropriate reference spectrum.