I am conducting a study on different image reconstruction algorithms for computed tomography (CT). My aim is to investigate which of the image reconstruction algorithms that have the highest signal-to-noise ratio (SNR). My dataset is 100 patients who underwent a CT brain scan. Each CT scan will be reconstructed with 4 different image reconstruction algorithms. Then I will measure the SNR for each algorithm and patient and compare the different reconstruction algorithms with regard to the SNR. So, we scan the patient's head and then the computer at once provides four different image reconstruction algorithms of the scan (4 different image sets) and then we measure the SNR of each image set and compare it to the other reconstruction algorithms (other image sets). Or, if it makes it easier for you to think. Consider the following corresponding scenario: You take a blood sample (corresponding to &quot;CT scan&quot;) from the patient and measure the glucose level with 4 different apparatus (corresponding to the 4 different image reconstruction algorithms). And then you compare the blood glucose level (corresponding to &quot;the SNR&quot;) between the four different apparatus. So, my question is if I should use a repeated measures ANOVA or just an ordinary one-way ANOVA. I am reposting my question because I have not received a definitive answer.
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I am conducting a study on different image reconstruction algorithms for computed tomography (CT). My aim is to investigate which of the image reconstruction algorithms that have the highest signal-to-noise ratio (SNR). My dataset is 100 patients who underwent a CT brain scan. Each CT scan will be reconstructed with 4 different image reconstruction algorithms. Then I will measure the SNR for each algorithm and patient and compare the different reconstruction algorithms with regard to the SNR. So, we scan the patient's head and then the computer at once provides four different image reconstruction algorithms of the scan (4 different image sets) and then we measure the SNR of each image set and compare it to the other reconstruction algorithms (other image sets). Or, if it makes it easier for you to think. Consider the following corresponding scenario: You take a blood sample (corresponding to &quot;CT scan&quot;) from the patient and measure the glucose level with 4 different apparatus (corresponding to the 4 different image reconstruction algorithms). And then you compare the blood glucose level (corresponding to &quot;the SNR&quot;) between the four different apparatus. So, my question is if I should use a repeated measures ANOVA or just an ordinary one-way ANOVA.
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I'm a little confused regarding the intraclass correlation coefficient and one-way ANOVA.  As I understand it, both tell you how similar observations within a group are, relative to observations in other groups.  Could someone explain this a little better, and perhaps explain the situation(s) in which each method is more advantageous?
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I develop an application in which i constantly get samples of heart pulse.  I defined an interval of t seconds.  In each t seconds I have n samples.  In every interval, I want to calculate the tendency of those n samples. For example, lets say I have n = 5, and I have samples with values {70, 88, 95, 103, 115}. I want to recognize I have a growth in the heart pulse, and I want to have some measure for the rate of grows/decrease/almost no change.  I thought on two approaches for solving this problem.   I calculate the linear approximation for the n samples using linear regression by applying least squares implemented by the normal equations. (I treat each sample as two coordinates vector with x coordinate as time and y coordinate as heart pulse). I get from the normal equations a linear function of the form y = mx+b and my measure for the tendency is the slope, i.e. the m value. The second approach is to calculate the correlation (pearson's correlation) between vector x and vector y when x is the time and y is the heart pulse.   I'm asking which approach do you think is better for my problem (determining the tendency of heart pulses). Or, do you have a better algorithm for solving this problem?
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I am working on the lab which is allowed to ask other people for hints.    In the image, program called "Audacity" is used to capture that waveform.  Question 1     In the image it says, "The peak-to-peak span of the signal is about 2.0 V"   It says its span range is 2.0 V, but I think that it spans from around -0.2 (lowest point in the wavefore picture) to +0.8 (highest point in the wavefore picture) according to picture. But why this description says it is 2.0 V?  Question 2     In the image it says, "the graph below can show a range of about 4 volts top-to-bottom"   Similarly, I think total range of top-to-bottom in the image is from -1.0 to +1.0, which I think 2V in total. But why this description says it is 4 volts?
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What kinds of effects are present in digital images that are referred to as "noise"?    What are the different sources of noise?  What causes each type of noise? What are the characteristics of the different types of noise? How do the different types of noise visually manifest in the image? (i.e., do different kinds of noise "look different" is the resulting image, and how would they differ to the eye?) How can you minimize each type? What different post-processing techniques are most appropriate for each different kind?
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There are two main probabilistic approaches to novelty detection: parametric and non-parametric. The non-parametric approach assumes that the distribution or density function is derived from the training data, like kernel density estimation (e.g., Parzen window), while parametric approach assumes that the data comes from a known distribution.  I am not familiar with the parametric approach. Could anyone show me some well known algorithms? By the way, can MLE be considered as a kind of parametric approach (the density curve is known, and then we seek to find the parameter corresponding to the maximum value)?
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I've got an application where it'd be handy to cluster a noisy dataset before looking for subgroup effects within the clusters.  I first looked at PCA, but it takes ~30 components to get to 90% of the variability, so clustering on just a couple of PC's will throw away a lot of information.    I then tried t-SNE (for the first time), which gives me an odd shape in two dimensions that is very amenable to clustering via k-means.  What's more, running a random forest on the data with the cluster assignment as the outcome shows that the clusters have a fairly sensible interpretation given the context of the problem, in terms of the variables that make up the raw data.  But if I'm going to report on these clusters, how do I describe them?  K-means clusters on principal components reveal individuals who are nearby to one another in terms of the derived variables that comprise X% of the variance in the dataset.  What equivalent statement can be made about t-SNE clusters?  Perhaps something to the effect of:     t-SNE reveals approximate contiguity in an underlying high-dimensional manifold, so clusters on the low-dimensional representation of the high-dimensional space maximize the "likelihood" that contiguous individuals will not be in the same cluster   Can anyone propose a better blurb than that?
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To increase the 12-bit resolution of ADC from 12 bit to 14 bit, this can be done through the 'oversampling and decimation method'. An  says that  The higher the number of samples averaged is, the more selective the low-pass filter will be, and the better the interpolation. The extra samples, m, achieved by oversampling the signal are added, just as in normal averaging, but the result are not divided by m as in normal averaging. Instead the result is right shifted by n, where n is the desired extra bit of resolution, to scale the answer correctly. Right shifting a binary number once is equal to dividing the binary number by a factor of 2. It is important to remember that normal averaging does not increase the resolution of the conversion. Decimation, or Interpolation, is the averaging method, which combined with oversampling, which increases the resolution  This reference clearly says that for the decimation method, the result is right shifted by the desired extra bit of resolution, and not divided by m as in the normal average.  So, the question is, why do we need to use the decimation method instead of the normal averaging after the oversampling to increase the ADC resolution?  It says above &quot;Right shifting a binary number once is equal to dividing the binary number by a factor of 2&quot;, but what if we don't use a binary number? How do we use the decimation method in this case?
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Context: I'm trying to understand the use of variational autoencoders as generators. My understanding:   During training, for an input point $x_i$ we want to learn latent $\mu_i$ and $\sigma_i$ and then sample $z_i \sim N(\mu_i, \sigma_i)$ and feed it to the decoder to get a reconstruction $\hat{x}_i = \text{decode}(z_i)$. But we can't do back propagation with sampling operator, so instead we reparametrize and use $z_i = \mu_i + \sigma_i \epsilon$ where $\epsilon \sim N(0, 1)$. Our reconstruction becomes $\hat{x}_i = \text{decode}(\mu_i + \sigma_i \epsilon)$.   However when we're done with training and ready to use it as generator, we sample $z \sim N(0, 1)$ and feed it to decoder: $x_{sample} = \text{decode}(z)$ .  The part that confuse me is that during training, the decode operation was done using $\mu_i + \sigma_i \epsilon$ which to my understanding this is using $N(\mu_i, \sigma_i)$ with different $\mu_i$ and $\sigma_i$ for each training example. However during the generation time, the decode operation is done (effectively) on $\epsilon$ alone from $N(0, 1)$. Why are we setting $\mu = 0$ and $\sigma = 1$ during generation (i.e. using $z = 0 + 1 \cdot \epsilon$)?
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I have some non-Gaussian distributed variable and I need to check if there are significant differences between the values of this variable in 5 different groups.  I have performed Kruskal-Wallis one-way analysis of variance (which came up significant) and after that I had to check which groups were significantly different. Since the groups are kind of sorted (the values of the variable in the first group are supposed to be lower than the values of the variable in the second group which are supposed to be lower than the values of the variable in the third group and so on) I only performed 4 tests:  Group 1 vs Group 2 Group 2 vs Group 3 Group 3 vs Group 4 Group 4 vs Group 5   I have performed this analysis with two different methods. I started by using Dunn's Multiple Comparison Test but nothing came up significant. On the other hand if I use Mann-Whitney test and correct for the number of tests (4) using Bonferroni, 3 tests come up significant.  What does it mean? Which results should I trust?
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I am new in remote sensing field. I sometimes got confused when I read about image pre-processing. Can someone please elaborate to me the difference and some example methods to do radiometric correction and radiometric calibration ?  Is converting DN values to Top Of Atmospheric (TOA) reflectance values from 2 sets of images (e.g Landsat 7) from different time counted as correcting or calibrating ? Are DOS (Dark Object Subtraction) and Sun-angle correction parts of radiometric correction ?
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An investigator wishes to produce a combined analysis of several datasets.  In some datasets there are paired observations for treatment A and B.  In others there are unpaired A and/or B data.  I am looking for a reference for an adaptation of the t-test, or for a likelihood ratio test, for such partially paired data.  I am willing to (for now) to assume normality with equal variance and that the population means for A are the same for each study (and likewise for B).
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I'm looking for recommendations on best practices for dealing with raster data layers with different resolutions and projections. The advice I've been given is to always resample to the layer with the lowest resolution before performing any analysis, but this seems like huge waste of precision to me and I've never been given a solid explanation for why it should be done.  When is it reasonable to resample to match a higher resolution grid and what are the implications compared to resampling to a lower resolution?  I realize that this is likely highly situation dependent. I'm mostly looking for general guidelines, but here's my specific scenario for reference:  Scenario: I'm looking to construct a spatial regression model predicting land use based on a variety of environmental and socio-economic layers. My land use map is Landsat derived and hence 30m resolution. Examples of explanatory layers include the  (3 arc-seconds, ~90m) and  climate layers (30 arc-seconds, ~1km).
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1) How do we decide if we split into 2 subnodes, or more? Or is it always 2?  2) How do we decide what threshold is the cutoff? Specifically, you have a continuous variable, do you do a binary search, or how is the cutoff decided?
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I have four numeric variables. All of them are measures of soil quality. Higher the variable, higher the quality. The range for all of them is different:  Var1 from 1 to 10  Var2 from 1000 to 2000  Var3 from 150 to 300  Var4 from 0 to 5  I need to combine four variables into single soil quality score which will successfully rank order.  My idea is very simple. Standardize all four variables, sum them up and whatever you get is the score which should rank-order. Do you see any problem with applying this approach. Is there any other (better) approach that you would recommend?  Thanks  Edit:  Thanks guys. A lot of discussion went into "domain expertise"... Agriculture stuff... Whereas I expected more stats-talk. In terms of technique that I will be using... It will probably be simple z-score summation + logistic regression as an experiment. Because vast majority of samples has poor quality 90% I'm going to combine 3 quality categories into one and basically have binary problem (somequality vs no-quality). I kill two birds with one stone. I increase my sample in terms of event rate and I make a use of experts by getting them to clasify my samples. Expert classified samples will then be used to fit log-reg model to maximize level of concordance / discordance with the experts.... How does that sound to you?
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I have 40 different images (1, ..40),( each one has 10 repetition " 40x10"),i should use one hot encoding for each image (the 40),  for example image (1) the one hote encoding will be encoding will be: [ 1 0 0 0 0 0 0.....40(0)],  for images 2 the one hot encoding will be : [ 0 1 0 0 0 0 0 ...40(0)],  since each image has 10 repetition, for example; for the 10 images of 1 ( they are for same object but with slight difference among them),  should  I use same code vector for the 10 repetition!!
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There are there groups (colA, colB, colC) representing three different measurement methods. The question is whether there is a difference between the three methods. To decide the question we perform experiments and measure the same thing with each method. The output of each method is a label not a value on a numeric scale. In addition, we do not have a control group so we do not know which method's output is the right one in the experiment. I solved the question in the way below  but I became uncertain whether it is a correct solution. I might have oversimplified the problem. Consequently, the chi-square approach used tests something else not what we want.  Data:             colA,    colB,    colC experiment1 label1,  label1,  label2 experiment2 label3,  label1,  label3 experiment3 label4,  label4,  label2 experiment4 label5,  label4,  label5 ...    My first approach, probably oversimplified:   As we do not know which label is correct and which not, we regard at first all the outputs of method A correct and compare them to the other two columns and count the same labels in the same experiments in the other columns, then we regard all the outputs of method B correct and then method C. So we get the label count below:   I. colA regarded as correct colA(4) colB(2) colC(2)  II. colB regarded as correct colA(2), colB(4), colC(0)  III. colC regarded as correct colA(2), colB(0), colC(4)   Then we compute a chi-square test for each, here II. and III. are the same. (There are more than 5 expected values in each column it is just the example to highlight the problem.) This way we get three p values for each test, from which we select the highest one to be on the safe side and decide whether the deviations between columns are likely to be caused by chance only.    My second approach would probably be:   The data same data transformed in a different format:                          label1, label2, label3, label4, label5 methodA (earlier colA)       1,      0,      1,      1,      1, methodB (earlier colB)       2,      0,      0,      2,      0, methodC (earlier colC)       0,      2,      1,      0,      1,   Here the expected values for each label would be greater than 5 with the real data. However, we do not want to test whether the distribution among the labels are caused by chance only but whether there is a difference between the methodA, methodB and methodC. Can Chi-Square be used here? What other tests would you propose to use to see whether there is a difference between the three methods?  What would be your solution?