Questions tagged [reconstruction]

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2
votes
1answer
127 views

What is the general formula for radon back projection for a javascript implementation?

I'm aiming to implement a simulation of computed tomography back projection in javascript/HTML5 canvas. Trying to figure the correct approach for doing a back projections and I have been studying the ...
0
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2answers
349 views

Random (Over) Sampling signal and perfect Reconstruction in Nyquist form?

Imagine we have band limited signal with bandwidth of $B$, so the required Nyquist rate would be $f_{nyq}>2B$ that is oversampled with rates $f_s$ where $f_s = M*f_{nyq}$ and $M$ is random and $M&...
3
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1answer
357 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
282 views

Interpolation formula for two dimensional signal reconstruction in the frequency domain from polar samples

In the book, Advanced Topics in Shannon Sampling and Interpolation Theory by Robert J. Marks II, one may find an interpolation formula for reconstructing a two dimensional signal from regular polar ...
0
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2answers
2k views

What is the difference between image restoration and image reconstruction?

I am new to image processing. I don't know whether this is the right place to ask, but what is the difference between image restoration and image reconstruction?
1
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1answer
583 views

Reconstructing Signal From Its Cyclic Autocorrelation

Can a signal be reconstructed from its cyclic autocorrelation? Specifically, if we know $$ R^{\alpha}(\tau) = \int{x(t)x^{\ast}(t-\tau)e^{-j2\pi\alpha t}\mathrm{d}t}, $$ can we reconstruct $x(t)\in\...
1
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1answer
75 views

Hybrid Sampling Scheme Idea?

I am facing a problem which I could not find any robust solution for . Assume we have a signal, $x$, composed of sum of a few sinusoidal. e.g. $$x=A_1\sin(\omega_1t+\phi_1)+A_2\sin(\omega_2t+\phi_2)+...
4
votes
1answer
526 views

Shannon interpolation formula for downsampled data with an “almost ideal” low pass filter

Let $x[n]$ be a discrete time signal with DFT given by $X(f)=\sum_n x[n]e^{-2\pi inf}$ supported on $[-1/2M,1/2M]$ with $f\in[-1/2,1/2]$. I can then down-sample to get $y[n]:=x[nM]$. Then, let $$\...
3
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0answers
1k views

Sinc interpolation formula for signal reconstruction in frequency domain from bipolar samples

As per the title, I was wondering if there was a $\operatorname{sinc}$ based interoplation formula for reconstructing a signal in the frequency domain which has been sampled with respect the bipolar ...
0
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1answer
122 views

How to choose an interpolation method for seismic ground motion signals

I am working with seismic ground motion records from the PEER database. They are acceleration measurements that are band limited to 50 Hz and sampled at 200 Hz. I use these records to drive an ...
1
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1answer
141 views

image reconstruction using a set of kernels

I try to be brief. For what I understood Convolutional Neural Network CNN for style-transfer extract/learn the main features of source Image. I think these features basically are Kernels (of different ...
0
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1answer
817 views

Two-View 3D reconstruction using the sparse Levenberg–Marquardt algorithm

I have trouble implementing the Levenberg-Marguardt algorithm as described in the book Multi View Geometry in Computer Vision. To be more specific I have trouble calculating the partial derivatives ...
1
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1answer
33 views

How to sample $f:=f_{1}\cdot f_{2}\cdot…\cdot f_{K}$?

Let $f_{k}$ be $\sigma_{k}$-bandlimited, $k=1,2,...,K$ and define $f:=f_{1}\cdot f_{2}\cdot...\cdot f_{K}$; then how should I choose $T>0$ such that we can recover $f$ from samples $f(nT)$? ...
0
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3answers
103 views

What algorithms can automatically determine a 3D scene from one or a few 2D images?

For a project I'm doing, I'm trying to model a scene based on a phone camera's video input, and then insert arrows into it that indicate direction in three dimensions. I've looked around, and this ...
1
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1answer
670 views

Does Zero Padding Work as Advertised?

I have trouble accepting the merits of zero padding in the frequency domain to give more points in FFT. Wonder if anyone else has similar thoughts. The mathematical 'proof'for the validity of zero ...
9
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3answers
554 views

Signal values we will 'miss' between sampling instances during sampling of band limited signals

According to the Nyquist–Shannon sampling theorem, any continuous time signal with a bandwidth $B$ smaller than Nyquist frequency $f_N=f_s/2$ (with $f_s$ the sampling frequency), which is sampled at ...
1
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1answer
139 views

Simulating noise in computed tomography reconstruction

In the research of the computed tomography (CT) reconstruction, one needs to simulate the noise during CT projection and capturing. Then, my questions are: How about the proper noise type? How to ...
2
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1answer
924 views

Computing sine phase and amplitude

I need to compute the DC offset, amplitude, and phase of a sine wave and I would like some help validating that my current technique is correct and get some tips to improve my technique. I am a DSP ...
0
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1answer
54 views

Question about MRI signal construction

As I understand it, in MRI, a line in k-space is usually acquired while the readout gradient is applied. So during the application of this gradient the protons spin at different frequencies along the ...
0
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1answer
642 views

MRI reconstruction using windowing based apodization

I am trying to apply windowing to do MRI reconstruction. I have a 256 point one dimensional k-space samples which look as follows: Here, the real part(green) is flat around 0 and the blue curve is ...
2
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2answers
152 views

Method of reconstructing a band-limited signal from discrete samples

I understand current cell phones use digital communications. Given that this industry brings in billions of dollars each year, there is much incentive to get the best performance possible. So what ...
1
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1answer
945 views

Upsampling and zero order hold

Maybe to someone this question may seem quite easy but I have a problem grasping it. Namely, assume that we have two systems A and B with sampling rates $f_A$ and $f_B$ where $f_A>f_B$ and $R=\frac{...
1
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1answer
173 views

Reconstruction of voice from distorted recordings

I would like to know how much of the sound of my voice getting through various types of walls can be reconstructed with easily obtainable software and algorithms. My plan is to place a microphone on ...
1
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1answer
130 views

How can a signal have two maximum frequency components?

$x(t)$ can be exactly reconstructed from its samples at $\omega_s = 10 \textrm{ rad/sec}$. My conclusion is that the maximum frequency component in $x(t)$ is $5\textrm{ rad/sec}$. But I'm being told ...
7
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1answer
4k views

Random sampling vs uniform sampling

In this paper of Lustig, he speaks about a something which appears unintuitive: sampling at random may exhibit better performance than sampling uniformly. I tried to understand this starting from page ...
1
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0answers
53 views

How to reconstruct 2D flat image from a series of pictures of a tube

I have pictures of an oesophagus (ie a tube) taken under standard white light looking down the tube. I have about 10 images taken over 20cm in series. The image looks forward down into the tube and ...
2
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2answers
260 views

image type after an ifft reconstruction

I reconstruct images from MRI k-space using ifft and root-sum-of-squares method. ...
1
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0answers
251 views

How to reduce reconstruction noise from a filtered back-projection reconstruction of a circularly symmetric image?

I need to perform tomographic reconstruction of an axially symmetric object. Because of the axial symmetry only one projection of the object (one angle) was taken. I implemented the filtered back-...
0
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2answers
1k views

Sample and reconstruct a real exponential (just one period)

I have a function with an equation: $$C = 1.6925\left( e^{-0.136t}-e^{-1.192t}\right) $$ Where $C$ is real and $t$ represents time in hours. Beneath is the representation of my function. I am ...
0
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2answers
762 views

Reconstruction of bandpass filtered signal from decimated version of itself

I know how to up-sample a discrete, real signal (by an integer factor n) that is band-limited to frequencies between $f_1 = 0 \mathrm{Hz}$ and and $f_2$: Just insert $n-1$ zeros between every original ...
0
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2answers
492 views

Ideal reconstruction after down sampling

The signal $x_a(t) = \cos(2\pi450t)$ is sampled. F = 450 Fs = 1000 Hz f = F/Fs = 450/1000 // Sampling theorem is fulfilled x(n) = cos(2*pi*(450/1000)) The ...
-1
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1answer
237 views

linear interpolator replacement for the sinc function

How to find an optimum linear interpolator replacement for the ideal sinc function? The reason is for the hardware implementation ease. For example when I use sinc interpolation: ...
0
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1answer
606 views

optimization of Image Reconstruction Algorithm using Genetic Algorithm in Matlab

I'm trying to optimize an image reconstruction algorithm using genetic algorithm.I took initial population size as 10.I have an input image an 10 reconstructed image.fitness function is the difference ...
0
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2answers
272 views

What is done to minimize distortion due to the hold operation?

A hold operation can be modeled using a step function over one sampling period i.e. $R(t) = 1/T * (h(t) - h(t-T))$, $h(t)$ the step function In frequency domain this is equivalent to $R(jw) = e^{-...
0
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1answer
184 views

Complex numbers in $\tt ifft$ of an MMSE amplitude estimator

I am trying to reconstruct a signal from a noisy speech using an MMSE algorithm proposed long time ago by Ephraim and Malah (1984). After going through the algorithm, I got a matrix A which represents ...
2
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2answers
1k views

Is magnitude information enough to reconstruct an audio signal

I have used an MMSE STSA estimator to obtain the magnitude of an audio signal. The original signal is combined with white noise and I used an algorithm given in an old research paper by Ephraim and ...
0
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0answers
904 views

What are the frequency components of a sampled signal after low-pass filtering?

A continuous signal $x_a(t)$ is a linear combination of sinusoids of frequency 250 Hz, 450 Hz, 1 kHz, 2.75 kHz and 4.05 kHz. The signal $x_a(t)$ is sampled at $f_s=$1.5 kHz, and the resulting digital ...
0
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1answer
5k views

Reconstructing time domain signal with Hanning window

I am currently working on a frequency domain real-time application on a digital signal processor. Currently for one time frame of my algorithm I read in time domain data into a buffer, perform a ...
1
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3answers
2k views

Are reconstruction filter always needed?

in mixed (digital and analogue application) where you have to convert a signal from continuous to digital time domain and then back again to continuous time an anti-aliasing LPF is needed and in ...
1
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1answer
190 views

Beyond cross-eyed 3D (VR application)

Making static 3D image is very simple - we just take image pair with something like this: then we can see 3D image by putting the left and right eye image side by side and crossing eyes or ...
5
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2answers
1k views

What Is the MATLAB `imreconstruct()` Useful For?

Could some one tell reasons to use the MATLAB imreconstruct function when processing images? I already have studied the topic and what the function actually does to ...
0
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1answer
269 views

Ideal Reconstruction of Upsampled Signal

Problem: The signal $cos(2\pi14100t)$ is sampled at $F_s = 400 Hz$. It is then upsampled with a factor 3 and then reconstructed ideally with a new frequency $F = 500 Hz$. I now want to find the new ...
1
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0answers
154 views

Calculate the intersample peak of a periodic sequence?

Similar to Calculating the PDF of a waveform from its samples, but for periodic sampled signals, and I just want the peak. Is there a way to calculate the highest inter-sample peak of the ...
1
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2answers
136 views

Computing shifted signal without first reconstructing

Looking for a solution to the following problem: A signal $x(t)$ is band limited to $B$ Hz, and sampled above the Nyquist rate, with corresponding $f_s = 1/T$. If the sampled signal is given by ...
0
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1answer
2k views

reconstruction of time series in SSA

i am trying to reconstruct time series from SSA ,because according to this link http://en.wikipedia.org/wiki/Singular_spectrum_analysis there is procedure ...
0
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1answer
374 views

Incoherence: Compressed Sensing (CS) vs Matrix Completion (MC)

I am seeking a clarification of the concept of Incoherence within the MC framework. Specifically, 1) the literature mentions the application of a "strong incoherence" given a set of assumptions. ...
2
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1answer
601 views

Reconstruct DWT for each cD1,cD2,cD3 and cA3 signals

This question must be basic for this forum, but I'm only start working with DWT recently, and I was working with CWT before. I ...
5
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0answers
173 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
2
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0answers
140 views

Upsampling Methods for Computed-Tomography

I have two sets of data of given Field of view, one of them only covers a subset of the FOV of the other. I therefore want to upsample the one with the larger FOV to combine it with the other one. So ...
0
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0answers
78 views

Reconstructing a partially deleted image through wavelets

I am trying to form an approximation of the wavelet transform from a partially sampled image. Reconstruction in the 1D case is easy. We have $w = h x$, with $w$ as the wavelet coefficients, $h$ as ...