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8

Signals 3 and 5 appear to be quite correlated -- they share their first harmonic. If I were given two mixtures of those, I wouldn't be able to separate those, I'd be tempted to put the common harmonic as one signal and the higher harmonics as a second signal. And I would be wrong! This might explain the missing eigenvalue. Signals 1 and 2 do not look ...


7

I'm not an expert on ICA, but I can tell you a little bit about independence. As some of the comments have mentioned, statistical independence between two random variables can be roughly interpreted as "the amount of information that observing one variable gives about another". However, because we're talking about statistical independence, all of this is ...


6

I am not a specialist in image processing but I highly doubt this is feasible with your requirements (single image, no prior information). The challenges is twofold: Detect which area of the image is a reflection. This looks like a quite complex scene understanding problem. In your example, I know that the right side is a reflection because I can infer from ...


6

There a few commercial algorithms that do exactly that (Dolby Prologic, DTS Neo 6, Lexicon Logic 7, Bose Videostage, etc.). If your project has the funds, you can simply try to license one of those. The inner workings of these algorithms are rather complicated and typically a mixture of time domain and frequency domain feature extraction, some steering ...


4

The model ICA uses says that there exist some unknown, statistically independent sources, $s_i$ that are non-normally distributed (their distributions are something other than Gaussian): $$ s_i \sim S(\mu_{s_i}, \sigma^2_{s_i}) $$ where $S$ is some (possibly) known but non-Gaussian distribution with mean $\mu_{s_i}$ and variance $\sigma^2_{s_i}$. Then it ...


3

As mentioned above, both signals 3 and 5 appear to be quite correlated and have a similar period. We can think of two signals being correlated if we can shift one of the sources left or right and increase or decrease its amplitude so that it fits on top of the other source. Note we are not changing the frequency of the source, we are just performing a phase ...


3

I would structure the thesis like this: Introduction/Problem Statement (i.e. whatever problem BSS solves) How BSS solves that problem (high level) Theory behind BSS 1) Definition of Independence of signals 2) Independence and correlation 3) PCA and other prewhitening methods: 1. centering 2. whitening Your implementation Your ...


3

You need to start as broad as possible and work your way towards your practical work. Your writing should make the case for the practical EVD work that you've done in matlab. After the start you posted you're going to need to need to cover bits about optimisation algorithms as well. FastICA, Infomax etc. Also different measures of independence: entropy, ...


3

I've taken this course. I think using these two papers plus those books you mentioned would be so useful in writing a report, thesis , ... . Blind signal separation: statistical principles Independent Component Analysis (A Tutorial) Also you could download my professor's thesis which is available online in this page


3

For your data set of images, first vectorize the images by raster scanning them, and making them vectors. Thus, say you have $M$ images, each of size 64*64 pixels. Then the total number of pixels per image is $N=64^2$, which means $N=4096$. Now, you have an image matrix of size $M\text{x}N$. For this image matrix, what you want to do is find the $M$ ...


3

One of the most successful uses of ICA has been in the study of electrophysiology (i.e. brain activity), principally EEG (Electroencephalography) and MEG (Magnetoencephalography). They are used to remove artefacts (such as electrical impulses caused by muscle movements (eye blinks etc)) without the need for reference channels. In this application the spatial ...


2

Rachel, From my research I have so far been able to find something called 'Chi-Squared Test For Independence', but I am not sure how it works at the moment, but it might be worth a look.


2

Your intuition is fine. But you may want to give a shot to a novel tecnique (GUSSS, Guided Underdetermined Source Signal Separation), described in this paper. The intuition is to extract an already known signal from another one. Let's say we have your EEG as $x$ and ECG as $s$: we can see $x$ as a mixture of the signal $s$ plus another mixture $\tilde{s}$ ...


2

I'm not a BSS expert, but it seems like a section on experimental results should probably follow. Once you've described PCA and other pre-whitening methods theoretically, it's good to show an example. It may be the case that you will include more subsections in your theoretical description, and that may prompt for more examples. Maybe someone else could ...


2

What you want to do is dimension reduction. The most basic, yet very powerful and commonly used, technique to do it is principal component analysis (PCA). PCA operates on the covariance matrix. You can look it up on Wikipedia for a throughout tutorial. PCA decomposes your data $y$, having dimension $d$, into $d$ principal components. The first principal ...


2

In the line C=(mnp*mnp')/3 you're dividing by 3 when you should really be dividing by the number of observations, which is 1000 in your case.


2

A very simple algorithm for stereo signals which are a combination of "panned" mono sources. This allows you to take a stereo source and "listen" to signals panned at a given point, or within a given range of the pan parameter. Caveats: It does not work well if the mix is more than a sum of panned mono sources (stereo reverb applied to the mix, tracks ...


2

In general, the topographic map describes the distribution of electrical activity across the brain as measured in a number of well known "stations" (electrodes whose position is known) on the scalp. This electrical activity is the combined result of millions of neurons firing below the skull. The strength of the electrical signal they create is measured ...


2

The matrices $\hat{\mathbf{M}}$ and $\tilde{\mathbf{M}}$ are constructed in such a way that the relation $\mathbf{M}\mathbf{x}=\mathbf{y}$ implies $\hat{\mathbf{M}}\hat{\mathbf{x}}=\hat{\mathbf{y}}$ and $\tilde{\mathbf{M}}\tilde{\mathbf{x}}=\tilde{\mathbf{y}}$. Consequently, for constructing the matrix $\tilde{\mathbf{M}}$, each element $m_{kl}$ of $\...


1

Removing the mean (and not the sum) from a linear filter leads to a filter that removes DC. For example: N = 10; h = [0.5 1 0.5]; conv(ones(N,1), h, 'valid') leads to 2s. N=10 h = [0.5 1 0.5]; h_high=h-mean(h); conv(ones(N,1), h_high, 'valid') leads to zeros. Alternatively, you can use any high pass filter.


1

The goal of FastICA is to rotate your data (unitary transform) so that each axis looks as non-Gaussian as possible. Gaussian data still looks Gaussian when you rotate it. If you don't "sphere" the data, all the algorithm can really do is rotate the whole block to one axis. By bringing the mean to zero (centering), and normalizing the variance in all ...


1

ICA can be seen as a dimension reduction technique similar to PCA. Although PCA consists of the eigenvectors of the covariance matrix i.e. second order statistics, ICA is not restricted and can contain higher order stat. The goal of ICA is to span the signal space in the most statistical independent vectors. So you might get a considerable dimension ...


1

If you just want to estimate the height of the square shaped component you can pass the composite signal thorough a low pass filter with a cut-off frequency close to DC or less than the minimum frequency you can expect to see in the composite signal apart from the square component. The resulting signal would have most of the non-DC components filtered out ...


1

This probably should be a comment, but I didn't earn that option yet. You can try measuring instrument impulse response. If I understand correctly, your system is essentially one-dimensional. Then if you use thin plate or plate of known thickness instead of thick object/material, your output signal will be an approximation of impulse response. Using it as ...


1

From your question, I take it that you are attempting to analyze, in a completely unsupervised way, unlabelled speech data so as to unveil two groups that should (hopefully) line up well with the "male" and "female" labels. Some notes: Cross-correlation is useless for speech application. The notion of speech similarity (be it at the higher level of the ...


1

One way is to synchronize Event related potentials(ERP) generator with your EEG measurement device. Alpha(8-13 Hz) potentials can be generated when the test subject closes the eyes and is in a relaxed state. Another ways is to flash black and white patterns at predetermined intervals. Literature can be easily found where many such techniques and related ERPs ...


1

How do I know I am not extracting noise (they are all very similar)? You should first find or record a well understood set of signals with which you can test your feature extraction code to verify your setup is correct and that the extracted components are as expected. Then you'll have higher confidence that you're not extracting noise due to errors in ...


1

The best way to compare your method to others is to run the algorithms on a common data set. Quntative measures such as PSNR vary significantly across images. It is also important to consider subjective analysis. After all, your research is aiming for improvements in appearance.


1

Read this paper about ISA: http://www.cs.helsinki.fi/u/ahyvarin/papers/ESANN06.pdf and this one about topographic ICA: http://www.cs.helsinki.fi/u/ahyvarin/papers/NC01_TICA.pdf Hyvärinen is the author of the FastICA algorithm. PS. By the way, you might want to look at ICASSO (http://research.ics.aalto.fi/ica/icasso/), if you are not already familiar ...


1

If you want to do source separation, then independent component analysis (ICA) is the correct technique, which you mention in the comments. ICA decomposes data as $x = As$ where $x$ are mixtures of some source signals $s$, and $A$ is the mixing matrix. Neither $A$ or $s$ is assumed to be known, ICA will find both of them given some $x$. The only assumptions ...


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