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DFT does not decompose a signal into regular sinusoids, it decompose it up into complex exponentials. Therefore, the Fourier transform of a real value signal must be conjugate symmetric (has both ...

Yes, at least in the above case it is possible. Though it might not be computationally as cheap as other methods such as least squares based curve fitting. I do not think injecting NaN gonna help, ...

My understanding of your question is that you have a small misunderstanding here. In the definition it is not said time and space. A signal can vary in time or space. Some signals vary with time, as ...

I'd like to point out Heisenberg Uncertainty principle, based on which theoretical achievable precision is limited. It states that one can not measure two complementary qualities (e.t. here time and ...

First of all, our brain does not only rely on our stereo visionary system to estimate the depth. There are many cues in a image scence for depth estimation, of which stereo, vision belongs to a sub-...

"Digital Signal Processing: A Computer-Based Approach" by Sanjit Mitra is what you need I guess, especially the exercises at the end of each chapter. There is a booklet on the Internet again by Mitra,...

As far as I understood, by image derivation you mean extracting edges. I would recommend to filter the image by a relatively large Gaussian filter. If computational cost of image derivation is ...

As far as I know there are two reasons: In sensing part: For practical implementation, usage of random matrices is hard, so people try to come up with simpler matrices that are fixed, this is thought ...

A sensing matrix maps input vector to measurement vector through linear wighted summation of input. What makes a specific matrix good, is application dependent. Now, both distributions more or less ...

Checking for RIP of a matrix is an NP-Hard problem which means it is not computationally feasible to accomplish. RIP is used in matrix design mostly in theoretical aspects. Stealing @David 's comments,...

Object detection is relatively a heavy task as you've notice. Detecting the object (in your case human face) in every and each frame would be cumbersome and computationally immense. Therefore, you ...

As far as I understood you're seeking the best similarity measuring function. There are zillions of metrics for that purpose, in fact any clustering algorithm such as SVM, K-means and neural network ...

First I explain how compressive sensing is leveraged into imaging reconstruction and then a little bit on how CS is deployed in an imaging hardware. Compressive Sensing For the sake of simplicity ...

You can use Hough Transform to find dominant lines in the image and then based on rho & theta parameters of the Hough transform, align your text. First you need to remove unnecessary details from ...

First,note that your drawn filter responses are one dimensional filters. Notch filter, selectively suppresses some frequency bands that are not of interest. One of the well known applications of ...

Compressive Sensing is an approach to reconstruct sparse signals from incomplete set of measurements. In doing so, we need to know $Ψ$ to recover $x$, don't we? yes, we do. But if we know $Ψ$,...

Since computing the optical flow for the whole image pixels is computationally immense, it it preferred to compute optical flow only around feature points. This method is called sparse optical flow. ...

The physical meaning is a signal passes through an LTI system! Convolution is defined as flip (one of the signals), shift, multiply and sum. I am going to explain my intuition about each. 1. Why we ...

It seems to me you have a little misassumption here. During the sampling only $\Phi$ matrix is applied to the signal $x$, which is resulted in measurements vector $y$, $y=Φx$ . Later, in ...

The other interesting approach which seems to be neglected in above answers is Deep Convolutional Neural Networks. It seems Google is using it right now for its image search engine and its translation ...

Two steps, do a simple histogram equalization to make the brightness a little bit more even. Then use canny edge detector (as suggested by Marcus Muller). matlab code: I=imread('Your Image'); G1=...

I think random sampling approach seems to be not effective, since the statistical population (pixel intensities) distribution in images is heavily localized. There might be more scientific approaches, ...

You can't prove RIP through numerical exploration of all possible cases. If you are interested in numerical analysis I suggest to use Coherence instead, however Coherence is not as strong condition ...

I spatial domain, simply convolve masks like averaging, or guassian with image to get low pass filtering: LowpassMask=(1/9)*ones(3,3); % Averaging mask of size 3*3 Filtered=conv2(image,...

My guess is you can find all rectangles using hough transform. OpenCV python returns a structure that has all rectangles. Then sort the rectangles and find take out the largest one and using the ...

It is not only noise. It is noise and distortion because this scenario modulates the signal as well. Abruptly changing amplitude of a signal is equivalent to multiplying the signal with a rectangular ...

Short answer, as a general rule NO, but depending on $g(t)$, in special cases YES, e.g. when $g(t)=0$ or $g(t)=Const$ ! Maybe if you find the Fourier of $Sign(G(f))$, e.g. $G(f)$ turns out to be ...

Curve fitting is another option after Fourier transform, you can fit a sum of sine function to your signal and the fitting coefficients show the amplitude and frequency of the signal. Check this: ...

It is necessary when reconstruction is considered. Simply imagine the case when $A = \Phi \Psi$ has a high coherence, e.g. all columns are exactly the same and indistinguishable, then there is no ...