# Questions tagged [inverse-problem]

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### Inverse FFT - Synch the Phase

Is there any way to synchronize phase of output of inverse DFT in each buffer? When I send the output of inverse DFT to the ...
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### Is Differentiation as a system, is an invertible system?

is the following system invertible? as I understand it, invertible means finding an inverse function which should return back the original input from an output of the given system. if so I ...
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### Are all LTI systems invertible? If not, what is a good counterexample?

I have been trying to figure this out for a while now. Everywhere I have looked I could easily find examples of invertible LTI systems, but I could not find any counterexamples. Can anybody shed some ...
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### Estimating Convolution Input Under the Assumption of Sparsity and Constant Non Zero Values Using Compressive Sensing Approach

I was wondering about if there is compressive sensing algorithm to estimate the sparse vector where the number of non-zeros values and amplitude of every non-zeros value are known. For example, assume ...
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### 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, ...
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### Whats the Correct Approach to Estimate the PSF of a Moving Detector

In lab, I did a bunch of scans using a radiation source and a detector. My source emits a gaussian beam (whose dimensions I know), and my detector is a uniform 7mmx7mm square. These are stationary and ...
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### Deconvolution of a 1D Signal with Known Kernel (Square Wave)

I have a signal measured from a radiation detector in a narrow beam of radiation. The peaks I get are quasi-gaussian in shape, see attached picture. The signal is not a function of time, rather a ...
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### Differences Using Maximum Likelihood or Maximum a Posteriori for Deconvolution / Deblur

Are there any differences if you use Maximum Likelihood or Maximum a Posteriori to estimate the Point Spread Function for image deconvolution?
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### How to Increase the Resolution of a Video from a Sequence of Photos?

I have a video filmed in a relatively low quality and resolution and a sequence of photos of higher quality taken of the same scene at the rate of about one image every two seconds or so. Could those ...
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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 ...
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### Solving equation with convolution

I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$: $$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$ where $\ast$ is the convolution. I know $A(f)$, $B(f)$,...
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### Extracting 'structure' post permutation

I have particle activity as shown in the left pane of animation below. The activity is clustered and it moves slowly. Sometimes these clusters merges together. On the right side of it, its shuffled ...
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### Estimate the Transfer Function of an Unknown System

Suppose you have a system, H, that you want to estimate its transfer function. You have a finite number of complex input samples, x, and noisy complex (magnitude and phase) output samples, y: In ...
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### 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 ...
759 views

### What Are the Differences between Super Resolution, Denoising and Deblurring?

In the fields of computer vision and image processing, what are the differences between Super Resolution, Denoising and Deblurring?
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### 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? ...
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### How Is the Formula for the Wiener Deconvolution Derived?

Wikipedia shows this formula: $$\ G(f) = \frac{H^*(f)S(f)}{ |H(f)|^2 S(f) + N(f) }$$ But how is this Wiener deconvolution formula derived and where does the squaring ($|H(f)|^2$) come from?
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### 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 ...
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### Deconvolution by Convolution

This is now a second time I am attempting to ask this very important but simple question here. What I want to know is can you do deconvolution by convolving a signal. It is often stated that, for ...
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### What Are the Types of Deconvolution?

I am totally new to image processing and wanted to ask you if you could confirm what I understood. It is about deconvolution: From what I read we find 2 main types of deconvolution: 1. Analytical <...
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### 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 ...
331 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'...
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### Why Is Super Resolution (SR) Possible?

I've been reading about Super Resolution Image reconstruction (Reconstruction of high resolution image from multiple low resolution aliased images contain sub pixel shifts), and i want to know why SR ...
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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 ...
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### Deconvolution Using Complex Division in The Frequency Domain

Consider these two signals: a = [1 1 0 0 0 0 0 0] b = [1 0 1 0 0 0 0 0] their convolution is c = a * b = [1 1 1 1 0 0 0 0] ...
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### 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 ...
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If $x^{-1}(t)$ and $y^{-1}(t)$ denote the integrals of x(t) and y(t) defined by $x^{-1}(t)=\displaystyle\int_{-\infty}^{t} x(\lambda)d\lambda$ $y^{-1}(t)=\displaystyle\int_{-\infty}^{t}y(\lambda)d\... 2answers 273 views ### Inverse Problem / Deconvolution with Pink Noise Hi I dived somewhat into deconvolution of systems which can be described as:$s(t) = o(t) * h(t) + n(t)$where$s$is my measured 1D time resolved signal,$o$is the original signal$h$is the ... 0answers 182 views ### Room Impulse Response Inverse Problem This article here talks about a room impulse response generator which takes the source and destination coordinates, sound speed, sampling rate, room dimension and wall reflection coefficients as input ... 1answer 171 views ### Underdetermined deconvolution of windowed output Consider a discrete 'blurred' output$h[t]$given by the convolution of filter$f[t]$and signal$g[t]$. This question considers recovering$g[t]$from a window (subset) of$h[t]\$. This causes the ...
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 full ...