Stimulus / rate reconstruction with Wiener Kernels.

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In summary, the conversation discusses the use of a Volterra expansion to estimate firing rates of a neuron based on a given stimulus. The condition for the best estimate is achieved through a mathematical formula involving the Wiener Kernel and the Fourier transform. The speaker is having trouble applying this in Matlab and is receiving an unexpected result. The conversation also mentions the use of xcorr and fft functions in this process.
  • #1
Beserra
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Hello.

I am having some trouble trying to reconstruct my firing rates using a Volterra expansion.
Basically it is known that , if :
s(t) = the value of a given stimulus at time t
r(t) = the firing rate of a neuron at time t

then we assume that a possible estimate of the firing rate can be achieved by
rest(t) = r_0 + ∫dτ D(τ)s(t-τ) where D(τ) is the Wiener Kernel.

Then the condition for the best estimate rest(t) is achieved when
FD(ω)*FQss(ω) = FQrs(-ω) . Where FA denotes the Fourier transform of a function A.

While I understand all this mathematically I can not apply it using Matlab.
I have s as a vector of positions of a given stimulus and rg as a vector of
rates of a neuron .

Then I make
QSS = xcorr(S,S);
QrS = xcorr(rg,S);
FQSS = fft(QSS);
FQrS = fft(QrS);
G = FQrS(length(FQrS):-1:1); % G(ω) = FQrS(-ω) because xcorr seems to put the t = 0
%at the middle of the vector
FD = G./FQSS'
D = ifft(FD);

When I make 'rest' proportional to 'conv(D, S)' I obtain not my firing rates but rather
a very similar version of my own stimulus S.

What am I doing wrong? Thanks!

Beserra
 
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  • #2
I forgot to specify that Qab denotes the cross correlation function of a and b
 

1. What is stimulus/rate reconstruction with Wiener Kernels?

Stimulus/rate reconstruction with Wiener Kernels is a mathematical technique used to estimate the underlying stimulus or input signal that leads to a particular response or output signal. This method is commonly used in neuroscience to uncover relationships between sensory stimuli and neural activity.

2. How does Wiener Kernel analysis work?

Wiener Kernel analysis involves using a series of filters, called Wiener Kernels, to map the input signal to the output signal. These kernels are determined by the relationship between the input and output signals and are used to reconstruct the input signal from the output signal.

3. What is the advantage of using Wiener Kernel analysis?

One advantage of using Wiener Kernel analysis is that it allows for both linear and non-linear relationships between the input and output signals to be identified. This allows for a more comprehensive understanding of the relationship between the two signals.

4. What types of data are suitable for Wiener Kernel analysis?

Wiener Kernel analysis is most commonly used with time series data, such as neural activity recordings, where there is a known input stimulus. It can also be applied to other types of data, such as audio signals, as long as there is a clear input-output relationship.

5. What are the potential applications of stimulus/rate reconstruction with Wiener Kernels?

Stimulus/rate reconstruction with Wiener Kernels has many applications in neuroscience, including understanding sensory processing, decoding neural activity to reconstruct visual or auditory stimuli, and predicting neural responses to different stimuli. It can also be used in other fields, such as signal processing and machine learning.

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