Questions tagged [inverse-problem]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2
votes
2answers
73 views

Inverse system of sinc?

I'm doing some self-study for an important exam I'll have in late March and came across the following question: So, using the convolution properties, if I want to find an identity system so that the ...
7
votes
2answers
179 views

Can Principal Component Analysis (PCA) Solve the Cocktail Party Problem?

I'm looking into the cocktail party problem and trying to figure out whether something like Principal Component Analysis is enough to separate out all the various voices at the cocktail party into its ...
3
votes
2answers
86 views

Deconvolution of a 1D Time Domain Wave Signal Convolved with Series of Rect Signals

I have a synthesized signal (the bottom of the following figure), which is the convolution of the input signal (at the top) and the objective function (in the middle). The intention is to retrieve the ...
1
vote
0answers
28 views

Adapting Richardson Lucy (RL) Deconvolution for Shot Noise Limited Coherent Imaging

I am an experimental physicist who is collecting a series of coherent imaging of trapped gas. If you are familiar with phase contrast imaging, you may understand what I mean by coherent imaging. The ...
2
votes
1answer
102 views

An invertible system with memory

Suppose $\mathcal{L}$ be invertible system with memory. Does $\mathcal{L}^{-1}$ have memory necessarily? Intuitively I think the answer is "yes". There are many examples showing that. For ...
2
votes
1answer
32 views

In computed tomography (CT), why is 'Inverse Problem of Radon transform' studied?

As I know, the Radon transform is a very important tool in CT by Beer's law. Thus, finding $f(x)$ of Radon transform $Rf(L):=\int_{L} f(x)dl(x)$ is helpful in CT. Nowaday, the Filtered back-projection ...
2
votes
1answer
40 views

Regularization for Inverse Problems using the Singular Value Decomposition (SVD)

I am reading these lecture notes on Optimisation and Inverse Problems in Imaging, and I have difficulties understanding how figures on page 20 (Figure 3.2) or page 21 (Figure 3.3). Precisely, I don't ...
2
votes
3answers
153 views

Deconvolving a 1d Signal Using a Lookup Table of Kernels

assuming I measure a signal that has different PSFs per position in time. for example: ...
0
votes
1answer
63 views

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 ...
3
votes
2answers
130 views

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 ...
0
votes
0answers
13 views

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 ...
3
votes
3answers
169 views

Estimating the Signal by Deconvolution with a Prior on the Filter Coefficients and the Signal Samples

Assume I have signal $y[n]$ which is a result of convolution between channel $h[n]$ and signal $x[n]$. which means: $$y[n] = h[n] \ast x[n]$$ where $\ast$ is the convolution operation The signal $...
3
votes
2answers
103 views

Deconvolution of an Image Acquired by a Square Uniform Detector

So, I acquired some images by scanning a radiation source with a square detector like in the following gif. Where the dashed grid represents reality, the 3x3 square my detector, and the 4x4 my ...
7
votes
4answers
2k views

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 ...
0
votes
0answers
43 views

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 $A(f)$, $B(f)$,...
2
votes
0answers
32 views

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 ...
1
vote
2answers
180 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 ...
0
votes
2answers
64 views

Partial Fractions

Attached is image with solution and my attempt. I am trying to calculate the coefficients for partial fractions expansion of the following: $$ H(e^{j\omega}) = \frac{ \frac{1}{3} e^{-j2\omega} }{(1-\...
7
votes
3answers
606 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, ...
2
votes
1answer
836 views

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 ...
3
votes
1answer
970 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?
2
votes
3answers
1k views

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] ...
4
votes
2answers
470 views

Auto-correlation function, an inverse problem

$x[n]$ is a complex function $n=0,1,2,\cdots,L-1 $ we assume $x[n]$ is periodic in its index: $x[n+L]=x[n]$ Its auto-correlation function $C[n]$ is uniquely defined as: $$ C[n]=\sum_{i=0}^{L-1} x[i+...
2
votes
1answer
492 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 ...
0
votes
1answer
123 views

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 ...
1
vote
1answer
914 views

How to find inverse of convolution integral?

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\...
3
votes
4answers
216 views

Estimate Filter Coefficients from the Result of Linear Convolution with a Known Signal

If I have samples of input say x(1:500) and it passes through FIR filter with 9 taps and some unknown coefficients. The output y(1:508) is also known. The aim is to estimate the filter response in ...
3
votes
0answers
192 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 ...
3
votes
1answer
576 views

How to Use the DFT (FFT) to Solve a Least Squares Regularization Problem (Inverse Problem)?

Let $X$ and $K$ be an image and a Point Spread Function (PSF), respectively. The blur image $B$ is obtained as follows $$B = X * K$$ I want to solve the following general regularization problem $$...
4
votes
1answer
183 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 ...
2
votes
1answer
1k 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 full ...
0
votes
1answer
125 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 ...
2
votes
1answer
329 views

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 <...
2
votes
1answer
333 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'...
1
vote
2answers
285 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 ...
2
votes
3answers
6k views

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 [...
5
votes
3answers
2k views

Estimating the Impulse Response of the Room Using Sweep Signal Microphone Recorded Signal (Input & Output of a Convolution)

I played this signal A (a 20Hz to 20000Hz sinusoidal sweep in 10 seconds) with a studio monitor speaker in a big church, and I recorded the result B with good microphones. The result is very reverb-...
3
votes
1answer
332 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 ...
2
votes
1answer
139 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 ...
4
votes
1answer
2k views

Use MATLAB to Restore a Signal from a Given Degraded Signal Using Tikhonov Regularization

Anyone could share how to develop an application in MATLAB to restore the signal from a given degraded signal using Tikhonov regularization i.e restoring the signal $f$ via solving $$ \min || g - f ...
2
votes
1answer
417 views

Deconvolution Using Response to an Heavy Side

I'm measuring a "charge" signal in function of time from an amplifier. Here is a measured signal (x-axis is the time in some arbitrary units, y-axis is the charge in ADU): I would like to get the "...
2
votes
1answer
117 views

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 ...
4
votes
1answer
4k views

1D Deconvolution with Gaussian Kernel (MATLAB)

Suppose that I know the output and the transfer functions of a system and I would like to calculate the input function using deconvolution. To get a grasp of the idea I have created a simple ...
1
vote
1answer
360 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? ...
6
votes
4answers
4k views

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 ...
4
votes
2answers
3k views

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 ...
4
votes
3answers
371 views

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 ...
2
votes
1answer
87 views

Why Does Image Deconvolution Still Work with Image without Sharp Edges?

Why does image deconvolution still work with image without sharp edges? Take this image for example:
2
votes
2answers
3k views

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?
3
votes
2answers
194 views

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 ...