Influence of noise and sampling rate on the discrete image representation error

Introduction: Digital registration of images is accompanied not only by an error caused by finite spatial resolution of the photo matrix, but also by the effect of noise whose contribution to the total error decreases with an increase in the aperture of the photosensors in the matrix. Thus, changing the sampling rate has the opposite effect on the sampling error and on the error caused by the noise. Purpose: Finding the optimal image sampling rate which would provide the minimum sampling error in the presence of noise. Results: We have studied how an image discrete representation error depends on the sampling frequency and noise level. The image sampling process in the presence of noise was simulated in the MATLAB environment. The dependencies of the root-mean-square deviation of the sampling error caused by spectrum truncation (decrease in the passband of the low-pass filter) and the noise component of the error on the sampling frequency were plotted. A theorem is formulated on the upper bound of the sampling theorem: when sampling a function of finite duration in the presence of noise, there is a finite minimum value of the sampling error which is determined by the shape of the spectrum of the function and the noise level. Practical relevance: It is advisable to use the research results when choosing a photomatrix by the number of pixels for recording images in the presence of noise, as well as when choosing a low-pass filter passband for primary processing of a digital image.

An Error Analysis of Orthographic Representation in Written Chinese Characters

This paper reports an error analysis of orthographic representation in written Chinese characters among Mandarin as foreign language (MFL) learners studying at an elementary level at a Malaysian public university in their dictation assessment. A total of 262 stroke error types of their orthographic representation in written Chinese characters were collected and analysed. The errors were consequently classified into four main categories among 165 MFL learners who took part in the study. The study found that participants made most mistakes in the stroke numbers and shape of orthographic representation in written Chinese characters. It was also found that there were detectable mistakes in stroke relation and stroke direction of orthographic representation in written Chinese characters. The cognitive factors contributing to the orthographic representation error types in written Chinese characters are discussed. It is concluded that beginner MFL learners would have a greater tendency to commit several character errors in writing Mandarin because of their low level of orthographic awareness and presumably a high cognitive load given to them as they transit from writing alphabets scripts to writing Chinese characters. Future research could examine how MFL learners cognitively adapt when transitioning from alphabet scripts to Chinese characters. Findings would guide instructors in the teaching Chinese characters more efficient and subsequently, it would allow them to interpret orthographic representations and write Chinese characters more accurately.

Calibrating a global atmospheric chemistry transport model using Gaussian process emulation and ground-level concentrations of ozone and carbon monoxide

Atmospheric chemistry transport models are important tools to investigate the local, regional and global controls on atmospheric composition and air quality. To ensure that these models represent the atmosphere adequately, it is important to compare their outputs with measurements. However, ground based measurements of atmospheric composition are typically sparsely distributed and representative of much smaller spatial scales than those resolved in models; thus, direct comparison incurs uncertainty. In this study, we investigate the feasibility of using observations of one or more atmospheric constituents to estimate parameters in chemistry transport models and to explore how these estimates and their uncertainties depend upon representation errors and the level of spatial coverage of the measurements. We apply Gaussian process emulation to explore the model parameter space and use monthly averaged ground-level concentrations of ozone (O3) and carbon monoxide (CO) from across Europe and the US. Using synthetic observations, we find that the estimates of parameters with greatest influence on O3 and CO are unbiased, and the associated parameter uncertainties are low even at low spatial coverage or with high representation error. Using reanalysis data, we find that estimates of the most influential parameter – corresponding to the dry deposition process – are closer to its expected value using both O3 and CO data than using O3 alone. This is remarkable because it shows that while CO is largely unaffected by dry deposition, the additional constraints it provides are valuable for achieving unbiased estimates of the dry deposition parameter. In summary, these findings identify the level of spatial representation error and coverage needed to achieve good parameter estimates and highlight the benefits of using multiple constraints to calibrate atmospheric chemistry transport models.

Sea surface salinity subfootprint variability from a global high-resolution model

Subfootprint variability (SFV) is variability at a spatial scale smaller than the footprint of a sat-ellite, and cannot be resolved by satellite observations. It is important to quantify and understand as it contributes to the error budget for satellite data. The purpose of this study is to estimate the SFV for sea surface salinity (SSS) satellite observations. This is done using a high-resolution (1/48°) numerical model, the MITgcm, from which one year of output has recently become availa-ble. SFV, defined as the weighted standard deviation of SSS within the satellite footprint, was computed from the model for a 2°X2° grid of points for the one model year. We present maps of SFV for 40 and 100 km footprint size, display histograms of its distribution for a range of foot-print sizes and quantify its seasonality. At 100 km (40 km) footprint size, SFV has a mode of 0.06 (0.04). It is found to vary strongly by location and season. It has larger values in western bound-ary and eastern equatorial regions, and a few other areas. SFV has strong variability throughout the year, with generally largest values in the fall season. We also quantify representation error, the degree of mismatch between random samples within a footprint and the footprint average. Our estimates of SFV and representation error can be used in understanding errors in satellite obser-vation of SSS.

Towards monitoring CO₂ source-sink distribution over India via inverse modelling: Quantifying the fine-scale spatiotemporal variability of atmospheric CO₂ mole fraction

The prospect of improving the estimates of CO2 sources and sinks over India through inverse methods calls for a comprehensive atmospheric monitoring system involving atmospheric transport models that make a realistic accounting of atmospheric CO2 variability. In the context of expanding atmospheric CO2 measurement networks over India, this study aims to investigate the importance of a high-resolution modelling framework to utilize these observations and to quantify the uncertainty due to the misrepresentation of fine-scale variability of CO2 in the employed model. The spatial variability of atmospheric CO2 is represented by implementing WRF-Chem at a spatial resolution of 10 km × 10 km. We utilize these high-resolution simulations for sub-grid variability calculation within the coarse model grid at a horizontal resolution of one degree (about 100 km). We show that the unresolved variability in the coarse model reaches up to a value of 10 ppm at the surface, which is considerably larger than the sampling errors, even comparable to the magnitude of mixing ratio enhancements in source regions. We find a significant impact of monsoon circulation in sub-grid variability, causing ~3 ppm average representation error between 12–14 km altitude ranges in response to the tropical easterly jet. The cyclonic storm Ockhi during November 2017 generates completely different characteristics in sub-grid variability than the rest of the period, whose influence increases the average representation error by ~1 ppm at the surface. By employing a first-order inverse modelling scheme using pseudo observations from nine tall tower sites over India and a constellation of satellite instruments, we show that the Net Ecosystem Exchange (NEE) flux uncertainty solely due to unresolved variability is in the range of 6.3 to 16.2 % of the total NEE. We illustrate an example to test the efficiency of a simple parameterization scheme during non-monsoon periods to capture the unresolved variability in the coarse models, which reduces the bias in flux estimates from 9.4 % to 2.2 %. By estimating the fine-scale variability and its impact during different seasons, we emphasise the need for implementing a high-resolution modelling framework over the Indian subcontinent to better understand processes regulating CO2 sources and sinks.

Calibrating a global atmospheric chemistry transport model using Gaussian process emulation and ground-level concentrations of ozone and carbon monoxide

Atmospheric chemistry transport models are important tools to investigate the local, regional and global controls on atmospheric composition and air quality. To ensure that these models represent the atmosphere adequately it is important to compare their outputs with measurements. However, ground based measurements of atmospheric composition are typically sparsely distributed and representative of much smaller spatial scales than those resolved in models, and thus direct comparison incurs uncertainty. In this study, we investigate the feasibility of using observations of one or more atmospheric constituents to estimate parameters in chemistry transport models and to explore how these estimates and their uncertainties depend upon representation errors and the level of spatial coverage of the measurements. We apply Gaussian process emulation to explore the model parameter space and use monthly averaged ground-level concentrations of ozone (O3) and carbon monoxide (CO) from across Europe and the US. Using synthetic observations we find that the estimates of parameters with greatest influence on O3 and CO are unbiased, and the associated parameter uncertainties are low even at low spatial coverage or with high representation error. Using reanalysis data, we find that estimates of the most influential parameter – corresponding to the dry deposition process – are closer to its expected value using both O3 and CO data than using O3 alone. This is remarkable because it shows that while CO is largely unaffected by dry deposition, the additional constraints it provides are valuable for achieving unbiased estimates of the dry deposition parameter. In summary, these findings identify the level of spatial representation error and coverage needed to achieve good parameter estimates and highlight the benefits of using multiple constraints to calibrate atmospheric chemistry models.

Jointly Learning the Discriminative Dictionary and Projection for Face Recognition

Recently, dictionary learning has become an active topic. However, the majority of dictionary learning methods directly employs original or predefined handcrafted features to describe the data, which ignores the intrinsic relationship between the dictionary and features. In this study, we present a method called jointly learning the discriminative dictionary and projection (JLDDP) that can simultaneously learn the discriminative dictionary and projection for both image-based and video-based face recognition. The dictionary can realize a tight correspondence between atoms and class labels. Simultaneously, the projection matrix can extract discriminative information from the original samples. Through adopting the Fisher discrimination criterion, the proposed framework enables a better fit between the learned dictionary and projection. With the representation error and coding coefficients, the classification scheme further improves the discriminative ability of our method. An iterative optimization algorithm is proposed, and the convergence is proved mathematically. Extensive experimental results on seven image-based and video-based face databases demonstrate the validity of JLDDP.

Feasibility Pump Algorithm for Sparse Representation under Gaussian Noise

In this paper, the Feasibility Pump is adapted for the problem of sparse representations of signals affected by Gaussian noise. This adaptation is tested and then compared to Orthogonal Matching Pursuit (OMP) and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The feasibility pump recovers the true support much better than the other two algorithms and, as the SNR decreases and the support size increases, it has a smaller recovery and representation error when compared with its competitors. It is observed that, in order for the algorithm to be efficient, a regularization parameter and a weight term for the error are needed.

Kesalahan Representasi Siswa dengan Kemampuan MatematikaTinggi dalam Menyelesaikan Masalah Perbandingan

<p><strong>Abstract: </strong>This study aims to describe the misrepresentation of students with high mathematical ability in solving comparative problems. This type of research is descriptive research. The subjects in this study were one grade VIII J student at SMP Negeri 1 Ngunut Tulungagung. In this study, data collection techniques used were tests to solve problems of comparison and interviews with students. Comparative test sheets and interview guidelines were used as instruments in this study. The results of this study are students with high mathematical ability to make visual and verbal representational errors at the step of understanding a problem. At the step of devising a plan, carrying out the plan and looking back the symbol representation error.</p><p><strong>Abstrak:</strong> Penelitian ini bertujuan untuk mendeskripsikan tentang kesalahan representasi siswa berkemampuan matematika tinggi dalam menyelesaikan masalah perbandingan. Jenis penelitian ini adalah penelitian deskriptif. Subjek dalam penelitian ini adalah satu siswa kelas VIII J di SMP Negeri 1 Ngunut Tulungagung. Dalam penelitian ini, teknik pengumpulan data yang digunakan adalah tes menyelesaikan masalah perbandingan dan wawancara dengan siswa. Lembar tes soal perbandingan dan pedoman wawancara digunakan sebagai instrumen dalam penelitian ini. Hasil penelitian ini adalah siswa yang berkemampuan matematika tinggi melakukan kesalahan representasi visual dan verbal pada tahap memahami masalah. Pada tahap merencanakan penyelesaian, melaksanakan rencana penyelesaian dan memeriksa kembali melakukan kesalahan representasi simbol.</p>