# Questions tagged [inverse-problem]

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### Increasing Image Resolution

I know of some oscilloscopes (DSA8300) that repeatedly sample at a few hundred kS/s to reconstruct a few GHz signal. I was wondering if this could be extended to 2D signals (photographs). Can I take a ...
2answers
5k views

### Using the Inverse Filter to Correct a Spatially Convolved Image

As part of a homework assignment, we are implementing the Inverse Filter. Degrade an image then recover with an Inverse Filter. I convolve the image in the spatial domain with a 5x5 box filter. I FFT ...
1answer
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### Deconvolution - Richardson Lucy vs Wiener Filter

I am studying some deconvolution techniques, In order to remove motion blur, like: Richardson-Lucy Wiener Are there any pros / cons of using one versus another? For example which are the pros / cons ...
3answers
266 views

### Deconvolution of Synthetic 1D Signals - How To?

I convolved a square wave with a Gaussian wave using linear convolution. Can I get the original square wave back by deconvolving my output with the Gaussian function? I took the FFT of both signals, ...
1answer
370 views

3answers
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### Deconvolution (Linear Convolution)with an Under Determined System of Equations?

If I have a measured signal $\mathbf{y}$ which is the result of the true signal $\mathbf{x}$ convolved with another function (linear and not circular convolution), I always seem to get an ...
1answer
2k views

1answer
461 views

### Is this system invertible or not?

Prove that the following system is invertible. $$y(t) = \mathcal{T}\{x(t)\} = \int_{-\infty}^{3t} x(\tau) \,\mathrm d \tau$$ Answer: yes, the system is invertible. I need some hint here, not the ...
0answers
128 views

### Room Impulse Response Inverse Problem

This article here talks about a room impulse response generator which takes the source and destination coordinates, sound speed, sampling rate, room dimension and wall reflection coefficients as input ...
2answers
62 views

### What Is the Relation Between Deblurring and Deconvolution in Computer Vision and Image Processing?

The deblurring problem can be modelled as follows $$f = \phi u + \epsilon, \; \epsilon \sim N(0, \sigma)$$ where $\phi$ is a filter (e.g. a low-pass filter) and $\epsilon$ is a Gaussian noise. In ...
1answer
265 views

### Why Sparse Priors Like Total Variation Opts to Concentrate Derivatives at a Small Number of Pixels?

When performing image deconvolution (deblurring), people often make use of priors to get rid of the illness of the problem. One very common prior is total variation, a sparse prior. Compared to ...
2answers
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1answer
287 views

### Intuitive Meaning of Regularization in Imaging Inverse Problems

Hello Every one I have been trying to understand the intuitive meaning of using a regularizer in images. Specifically what does the Total Variation regularizer do in images and how is it able to ...
1answer
88 views

### Phase error correction for Fourier transform basis vectors

I was wondering what is the best way to account for phase noise in a set of basis vectors? Example: I have a measured signal, say $f'(x)$ that should be related to a desired spectrum $f(\nu)$ through ...
1answer
306 views

### Best (Perceptually / Objectively) Super Resolution Methods Out There?

I'm curious about the advances in the area of image super-resolution (SR) that have given the best results to date, both perceptually (visually pleasing) and objectively (e.g. PSNR, SSIM criterias). I'...
1answer
128 views

### What are Local and Global Inpainting Techniques in Image Processing?

Is Diffusion-based inpaiting Local or Global? Is Pixel-based inpaiting Local or Global? Is Patch-based inpaiting Local or Global? Can Local-diffusion be used inside Patch-based in-painting problems of ...
1answer
88 views

### Inverse FFT - synch the phase

Is there any way to synchronise phase of output of inverse DFT in each buffer? When I send the output of inverse DFT to the speaker it sounds nasty. Of course I know the „windowing functions” but it ...
1answer
274 views

### Sharpen Defocused Image (Deconvolution / Image Restoration)

Using OCR, I want to extract text from product packages using Google Glass. However, because of the fixed focus of the camera the package pictures are blurred. Is there a way to sharpen the image? ...
3answers
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### Deriving the Convolution Kernel of the Inverse of a Signal

Let $y$ be the inverse (in the sense of convolution) of $x$, i.e. $$x \star y = \delta$$ Context: $x[n]$ is a discrete signal defined for $n = 0,\ldots, N$. We can assume $x[n] = 0$ if \$n \not\in [...