Mean Square Error Accuracy Research Articles

ENSURE: A General Approach for Unsupervised Training of Deep Image Reconstruction Algorithms.

Image reconstruction using deep learning algorithms offers improved reconstruction quality and lower reconstruction time than classical compressed sensing and model-based algorithms. Unfortunately, clean and fully sampled ground-truth data to train the deep networks is often unavailable in several applications, restricting the applicability of the above methods. We introduce a novel metric termed the ENsemble Stein's Unbiased Risk Estimate (ENSURE) framework, which can be used to train deep image reconstruction algorithms without fully sampled and noise-free images. The proposed framework is the generalization of the classical SURE and GSURE formulation to the setting where the images are sampled by different measurement operators, chosen randomly from a set. We evaluate the expectation of the GSURE loss functions over the sampling patterns to obtain the ENSURE loss function. We show that this loss is an unbiased estimate for the true mean-square error, which offers a better alternative to GSURE, which only offers an unbiased estimate for the projected error. Our experiments show that the networks trained with this loss function can offer reconstructions comparable to the supervised setting. While we demonstrate this framework in the context of MR image recovery, the ENSURE framework is generally applicable to arbitrary inverse problems.

Auto-detection of cervical collagen and elastin in Mueller matrix polarimetry microscopic images using K-NN and semantic segmentation classification.

We propose an approach for discriminating fibrillar collagen fibers from elastic fibers in the mouse cervix in Mueller matrix microscopy using convolutional neural networks (CNN) and K-nearest neighbor (K-NN) for classification. Second harmonic generation (SHG), two-photon excitation fluorescence (TPEF), and Mueller matrix polarimetry images of the mice cervix were collected with a self-validating Mueller matrix micro-mesoscope (SAMMM) system. The components and decompositions of each Mueller matrix were arranged as individual channels of information, forming one 3-D voxel per cervical slice. The classification algorithms analyzed each voxel and determined the amount of collagen and elastin, pixel by pixel, on each slice. SHG and TPEF were used as ground truths. To assess the accuracy of the results, mean-square error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) were used. Although the training and testing is limited to 11 and 5 cervical slices, respectively, MSE accuracy was above 85%, SNR was greater than 40 dB, and SSIM was larger than 90%.

Prediction Of The Number Of Tourists To Visit Bali Province Using Backpropagation Artificial Neural Network (Case Study: Data 1990-2016)

Bali Island is the most popular tourist destination in Indonesia. The total number of foreign tourists visiting Indonesia through the entrance of Ngurah Rai Airport reached 40% as of October 2016, with the value of Bali's foreign exchange receipts for Indonesia from the tourism sector amounting to 70 Trillion Rupiah. Minister of Tourism (Menpar) Arief Yahya always uses the password "Bali" in promoting destinations throughout the world. Because in tourism, Bali is a gate that is passed by 40 percent of foreign tourists (tourists) to Indonesia. In support of more accurate decision making, the author makes a system of forecasting numbers of foreign tourists visiting Bali Province by taking a sample of Japan. Factors that are used as input to make predictions include the number of tourists visiting before, the population of the country of origin of foreign tourists, Gross Domestic Product, and the Relative Consumer Price Index of the countries of origin of foreign tourists. In this research, optimization of the activation function, hidden neuron, and learning rate parameters is performed. Forecasting results using the backpropagation method produce a pretty good accuracy with an accuracy of Mean Square Error = 0.0050558, and test data accuracy of MSE = 0.031695. ANN architecture in the training process is then used to calculate predictions of visits by foreign tourists in the testing process

Application of soft computing models in streamflow forecasting

The accuracy of five soft computing techniques was assessed for the prediction of monthly streamflow of the Gilgit river basin by a cross-validation method. The five techniques assessed were the feed-forward neural network (FFNN), the radial basis neural network (RBNN), the generalised regression neural network (GRNN), the adaptive neuro fuzzy inference system with grid partition (Anfis-GP) and the adaptive neuro fuzzy inference system with subtractive clustering (Anfis-SC). The interaction between temperature and streamflow was considered in the study. Two statistical indexes, mean square error (MSE) and coefficient of determination (R2), were used to evaluate the performances of the models. In all applications, RBNN and Anfis-SC were found to give more accurate results than the FFNN, GRNN and Anfis-GP models. The effect of periodicity was also examined by adding a periodicity component into the applied models and the results were compared with a statistical model (seasonal autoregressive integrated moving average (Sarima)) to check the prediction accuracy. The results of this comparison showed that periodicity inputs improved the prediction accuracy of the applied models and, in all cases, the soft computing models performed much better than the Sarima model. The periodic RBNN and Anfis-SC models increased the MSE accuracy of Sarima by 25·5–24·7%.

Image Denoising Games

Based on the observation that every small window in a natural image has many similar windows in the same image, the nonlocal denoising methods perform denoising by weighted averaging all the pixels in a nonlocal window and have achieved very promising denoising results. However, the use of fixed parameters greatly limits the denoising performance. Therefore, an important issue in pixel-domain image denoising algorithms is how to adaptively choose optimal parameters. While the Stein's principle is shown to be able to estimate the true mean square error (MSE) for determining the optimal parameters, there exists a tradeoff between the accuracy of the estimate and the minimum of the true MSE. In this paper, we study the impact of such a tradeoff and formulate the image denoising problem as a coalition formation game. In this game, every pixel/block is treated as a player, who tries to seek partners to form a coalition to achieve better denoising results. By forming a coalition, every player in the coalition can obtain certain gains by improving the accuracy of the Stein's estimate, while incurring some costs by increasing the minimum of the true MSE. Moreover, we show that the traditional approaches using same parameters for the whole image are special cases of the proposed game theoretic framework by choosing the utility function without a cost term. Finally, experimental results demonstrate the efficiency and effectiveness of the proposed game theoretic method.

A Parcel-Scale Coastal Flood Forecasting Prototype for a Southern California Urbanized Embayment

Stanley, J.-D. and Corwin, K.A., 2013. Measuring strata thicknesses in cores to assess recent sediment compaction and subsidence of Egypt's Nile Delta coastal margin. Coastal flood risk in California is concentrated around urbanized embayments that are protected by infrastructure, such as levees, pumps, and flood walls, which pose a challenge to accurate flood prediction. A capability to predict coastal urban flooding at the parcel-scale (individual home or street) from high ocean levels (extreme high tides) is shown here by coupling a regional ocean forecasting system to an embayment-scale hydrodynamic model that incorporates detailed information about flood defenses. A unique flooding data set affords the rare opportunity to validate model predictions and allows us to identify model data that are essential for accurate forecasting. In particular, results show that flood defense height data are critical, and here, that information is supplied by a Real Time Kinematic Global Positioning System (RTK-GPS) survey, which yields ca. 1-cm, vertical root mean-squared error accuracy. Bathymetry surveys and aerial Light Detection and Ranging (LIDAR) data characterizing the embayment also prove essential. Moreover, hydrodynamic modeling of flood inundation is shown to significantly improve on planar surface models, which overestimate inundation, particularly when manipulated to account for run-up in a simplistic way. This is attributed to the transient nature of overtopping flows and motivates the need for dynamic, spatially-distributed overtopping models that are tailored to the urban environment.

Task-oriented quantitative image reconstruction in emission tomography for single- and multi-subject studies

Task-based selection of image reconstruction methodology in emission tomography is a critically important step when designing a PET study. This paper concerns optimizing, given the measured data of the study only, reconstruction performance for a range of quantification tasks: finding the mean radioactivity concentration for different regions of interests (ROIs), different ROI sizes and different group sizes (i.e. the number of subjects in the PET study). At present, the variability of quantification performance of different reconstruction methods, according to both the ROI and group sizes, is largely ignored. In this paper, it is shown that both the ROI and group size have a tremendous impact on the error of the estimator for the task of ROI quantification. A study-specific, task-oriented and space-variant selection rule is proposed that selects a close to optimal estimate drawn from a series of estimates obtained by filtered backprojection (FBP) and different OSEM (ordered subset expectation maximization) iterations. The optimality criterion is to minimize an estimated mean square error (MSE), where the MSE is estimated from the data in the study using the bootstrap resampling technique. The proposed approach is appropriate for both pixel-level estimates and ROI estimates in single- and multi-subject studies. An extensive multi-trial simulation study using a 2D numerical phantom and relevant count levels shows that the proposed selection rule can produce quantitative estimates that are close to the estimates that minimize the true MSE (where the true MSE can only be obtained from many independent Monte-Carlo realizations with knowledge of the ground truth). This indicates that with the proposed selection rule one can obtain a close to optimal estimate while avoiding the critical step of selecting user-defined reconstruction settings (such as an OSEM iteration number or the choice between FBP and OSEM). In this initial 2D study, only FBP and OSEM reconstruction methods are considered but the proposed selection rule should readily generalize to different estimators (i.e. different reconstruction algorithms) and 3D imaging.

A global least mean square algorithm for adaptive IIR filtering

In this brief, we develop a least mean square (LMS) algorithm that converges in a statistical sense to the global minimum of the mean square error (MSE) objective function. This is accomplished by estimating the gradient as a smoothed version of the MSE, The smoothed MSE objective begins as a convex functional in the mean. The amount of dispersion or smoothing is reduced, such that over time it becomes the true MSE as the algorithm converges to the global minimum. We show that this smoothing behavior is approximated by appending a variable noise source to the infinite impulse response (IIR)-LMS algorithm. We show, experimentally, that the proposed method does converge to the global minimum in the cases tested. A performance improvement over the IIR-LMS algorithm and the Steiglitz-McBride algorithm has been achieved.