# Questions tagged [inverse-problem]

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### Deconvolution using Toeplitz matrices [duplicate]

Lets say I have 2 vectors (1D signals that are sigmoids): $s$ and $m$, both related through the relation: $m = s * r$, my goal here is to recover the vector $r$ (should look like a gaussian). I tried ...
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### Academic reference for a specific type of regularized inverse filtering

Let $y(t) = (h * x)(t) + n(t)$ be some observed signal where $h(t)$ is some filter / impulse response, $x(t)$ is some input signal we are interested in, and $n(t)$ is noise. In order to recover $x$ ...
217 views

### Get the inverse transfer function from the measured response

What is a numerically stable way to obtain the inverse transfer function from a measured response? I have a system that shows a low-pass behavior. I would like to increase the bandwidth by some form ...
163 views

### Reconstructing a signal from a Nyquist plot

I have a system which is like a blackbox which has just one input which could be a sinusoidal wave which is a sum of a range of frequencies, now the problem is that I dont have the time-domain output ...
162 views

### How to compute the inverse Z-transform

How to compute the inverse Z-transform of the form $$G(z)=\frac{z^{2n}}{a(z^{2n})+b(z^n)+c}$$ I started by taking $$F(z^n)=G(z)$$ so $$\frac{F(z)}{z}=\frac{z}{az^2+bz+c}$$ This can be solved ...
122 views

### Is the system $y\left(t\right)=\int _{t^3-1}^{t^3}x\left(s\right)ds\:$ invertible? [duplicate]

I have the following system: $$y\left(t\right)=\int _{t^3-1}^{t^3}x\left(s\right)ds\:$$ I was told to determine if it's invertible system, casual system, memoryless system and linear system. I was ...
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### How to use inverse 2D Fourier transform to reconstruct the original image?

I have managed to get the forward Fourier transform of an image to the frequency space like so: But I cannot for the life of me reconstruct the original image from the inverse Fourier transform of ... 84 views

### Why does sign ambiguity occur in ICA?

I do not really understand the source of sign ambiguity in ICA. First, my understanding that If I apply ICA on a signal $X$ and I got 3 ICs which are represented by a set $IC^1$. Then, applying ICA on ...
169 views

### Image / Video Upscaling (Super Resolution) Algorithm Explanation (Image and Video Upscaling from Local Self Examples)

So, I'm trying to implement the classical algorithm described in this paper Image and Video Upscaling from Local Self-Examples and this presentation to serve as a baseline for comparison with AI/NN-...
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### Blind source separation for asynchronously observed mixture channels

Given your practical and theoretical expertise: Does ICA work reliably when applied to a multidimensional mixture (observation) $X = (X^1, \cdots, X^d)$ if the different channels $X^i$ of the ...
553 views

### Is a neural network an adaptive filter?

I am confused as to the difference between neural networks and adaptive filters: As far as I understand it, "neural networks" are largely used for solving inverse problems, where an unknown ...
71 views

### Identifying a signal by its power spectrum

Background: There is a method in optics for determining the electric field of light (both intensity and phase) via a three step process: Add a known phase shift to the light (called the "...
685 views

### Reconstruction of a Signal from Sub Sampled Spectrum by Compressed Sensing

Context Attempting to reproduce an illustrative example of compressive sampling from Candes-Wakin 2008. Specifically, the L1 recovery of a sparse signal shown on pg 5 in Fig. 2. Using my code (below), ...
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### Estimate the Image Using Multi Realizations of Its Convolution with a Known Filters Using Wiener Filter

Suppose we have a corrupted image $Y = H*X + \epsilon$ formed by taking an image $X$, convolving it with a point-spread function $H$, and adding gaussian noise $\epsilon$. Then we know that the Wiener ...
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### Cocktail Party Problem with a Single Signal of Data (Single Mic)

I have been doing some multimodal signal analysis, and sometimes ICA is used for detecting statistically independent components. From my understanding, say if you have 2 sources and 2 receivers/...
481 views

### Solve Efficiently the 1D Total Variation Regularized Least Squares Problem (Denoising / Deblurring)

How to solve a 1D Least Squares with Total Variation Regularization? I know gradient based methods, I wonder how much faster / efficient I can get.
120 views

### How Could One Accelerate the Convergence of the Least Mean Squares (LMS) Filter?

How can the convergence of an LMS filter be accelerated? Can we do better than the Vanilla algorithm?
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### Sparse FFT of ramp using zero padding

I would like to sparsely represent a linear function/ramp in the Fourier domain. In an attempt to improve the sparsity, I have zero padded it. With this padding, it is possible in the example I tried ...
337 views