Questions tagged [optimization]
The optimization tag has no usage guidance.
162
questions
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To find the unitary matrix which is the null of the results of multiplication with another matrix
I have a matrix $F ∈ \mathbb{C}^{(m × N)}$, where $m < N$, and $F \times F^H$ is a unitary $m × m$ matrix.
I need to find a unitary matrix $G$ with a dimension of $N × N$ such as results of $F\...
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Reference signal minimizes the MSE across similar signals with delays
I am dealing with the following problem:
I have $M$ signals ($x_1, x_2, \cdots, x_M$), each of length $N$, which are supposed to be similar, up to a certain delay between them and noise. I am ...
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Least squares filter with non-linear phase and independent weights for phase and magnitude
Intro
My question is related to a previous one linked here.
I am interested in non-linear phase FIR filters with a specific desired phase response.
After I tried the options in the linked question I ...
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1
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66
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Using MATLAB's `fmincon()` Solver for Linear Optimization Problem
If I have a linear optimization problem to be solved, is it correct to use the FMINCON SOLVER? If not, why?
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55
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Half-band FIR filter is not filtering as expected
I recently discovered that one may be able to further optimize an FIR filter processing time by skipping calculations of coefficients whose values are zero, providing that the filter is about halving ...
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105
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How to regularize the latent variables of a kalman filter to be small?
This is perhaps a bit of a weird idea but suppose I want the latent variables of a Kalman filter to be small (like as if the states were being regularized). This is kind of like putting an extra prior ...
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334
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Gradient descent algorithm not converging
I wish to use the gradient descent algorithm to minimize the cost function
$$J(\mathbf{w}) = (\mathbf{w} - \mathbf{w}_{o})^{T} \mathbf{A}(\mathbf{w} - \mathbf{w}_{o})$$
where $\mathbf{w} \in \mathbb{R}...
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155
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How to solve optimization problem
I am a newbie in Optimization. I have this Optimization problem, could anyone help how can I analyze it and solve it?
\begin{align}\label{Problem_formulation}
\mathbb P_1& ~~~~~~\mathop{\max}_{{ \...
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3
votes
1
answer
117
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Solving regularized least squares problem using black-box computation of $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T\mathbf{x}$
Let $\mathbf{A} \in \mathbb{R}^{n \times n}$. I'm working in a problem where I have a black-box algorithmic solution to compute the products $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T \mathbf{x}$ given ...
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54
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OFDM channel estimation using the transmitted signal multiplied with a matrix
I have OFDM system, where the modulated signal $x$ with length $N$, and $N$ is the number of subcarriers in OFDM symbol. $x$ is multiplied with a well-known unitary matrix $G \in N \times N$ before ...
- 165
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64
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L1 regularization vs maximal entropy?
Solving for ill-posed linear models, I saw that Maximal entropy is also parsimonious and in that regards similar to L1-sparsity promoting regularization. How is it different and are they ...
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151
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What is the best coding strategy?
There is a dataset of $N$ elements, each represented by $K$ bits. Now due to hardware limitations to reduce memory for storage, they have to be reprocessed into $K'$ bits each, and $K'<K$. What is ...
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49
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Optimization Problem in Graph Signal Processing to find edge weights
I am working on an application which consists of cross-roads and roads that connects them. In my design, I am using graph signal processing to estimate the importance of the roads which means edge ...
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32
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TDoA self-calibration with a single calibration emitter
I've recently asked a similar question aiming at the same problem on
Math.SE, for which I've set a bounty.
Problem.
I have a radio calibration transmitter with known fixed location $\langle t_x, t_y, ...
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1
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316
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Finding rectangle corners by using point cloud
I have a rectangle in the 3D scene, which I know its width and height. It is placed in the 3D scene like the image below. I can manually select all points on the rectangle by mouse click.
Given the ...
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Solve optimization problem to find nxn topelitz kernel C? [closed]
The optimization problem is to find $n \times n$ matrix $C$ such that $\left| \left| x - d C \right| \right|_{2}^{2}$ is minimised where $x$ is $1 \times n$ and $d$ is $1 \times n$. Is this possible ...
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2
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107
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FFT to work out optimum number of samples to average
I have a magnetometer, a LIS3MDL to be precise, and I am taking readings from it every second. As expected there is variation in the readings. For example, if I take five readings I get:
1164,
1190,
...
- 3
2
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42
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constructing a weighted penalty function as function of position for elastic net
I am solving a "special" elastic net like regularized least squares problem
$$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_2 + \lambda_1 {\...
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2
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370
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Constrained Least Squares Filter Design
I would like to design a complex FIR filter, $h$, for a known signal that produces a desired output: $d$ = $s*h$ (where $s$ is my signal and $d$ is the desired filter output). Let $S$ be the ...
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56
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How to interpret arg min in the the following equation?
I am studying the following equation:
$$\hat{s}_m(n) = \arg \min_{s_m(n)\in A_s}\left| \frac{\psi_m^H}{||\psi_m^H||^2}y_m(n)-s_m(n)\right|^2\tag{1}$$
here $A_s$ is 1x$N$ vector of QPSK symbols, $s_m(n)...
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Why expected value is optimal?
The expected value is widely used and considered optimal. The question is why it is optimal. The Wikipedia page or other google search on the topic does not clearly state why and under what condition ...
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153
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What procedure to find the parameters of a given filter prototype to fit a desired frequency response?
To model the frequency response of a system, I am looking for a method to fit the response of cascaded bi-quad filters to the response of that system using an optimization algorithm. The $S$-domain ...
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138
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Non-rectangular meshgrid in MATLAB
I want to create a non-rectangular meshgrid in matlab.
Basically I have a polygon shaped feasible set I need to make a grid of in order to interpolate 3D data points in this set. The function for ...
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2
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323
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Optimize window length (STFT) via gradient descent (in neural networks)
The authors from this paper optimized a Gaussian window size via gradient descent (the σ parameter of the bell curve) together with the other parameters of neural networks.
I don't use Gaussian window ...
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52
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Complexity of ZF precoding at the transmitter
If we have a modulated signal $s$ and ($m\times n$) MIMO channel $H$ where $m$ and $n$ are number of receive and transmit antenna, respectively. The ZF pre-coded signal is
\begin{equation}
x=Fs
\end{...
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65
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Is it possible to use a genetic algorithm for finding the correlation among time series
I am working on an optimized method for measuring the similarity between 2 signals, Is it possible to use a genetic algorithm for finding the correlation among time series?
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55
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Find similarities between 2 signals
Is there any heuristic method to find metrics, similarities between two signals?
I am not talking about correlation.
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100
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Adding Variance \ Weights Information When Solving a Basis Pursuit Denoising Problem (BPDN)
Having a "measured" vector $\mathbf{y}$ with its statistics (counts or variance per element), one can use weighted least squares approach to solve the linear system $$\mathbf{A}\mathbf{x} = \...
- 606
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345
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Why an does an integrate-and-dump stage in a CIC filter provide the same functionality as the integrator and comb in series?
I have a hard time understanding why the combination of integrator and comb (integrate-and-dump) is the same as a separate integrator and comb in series like in this picture:
Please explain why these ...
0
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1
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161
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Solve Efficiently the 1D $ L_1 $ Regularized Least Squares Problem (Denoising / Deblurring)
How to solve a 1D Least Squares with $ L_1 $ Regularization?
I know gradient based method, I wonder how much faster / efficient I can get.
Related to Solve Efficiently the 1D Total Variation ...
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244
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Correlation and the Fourier transform
In the book Fundamentals of Music Processing: Audio, Analysis, Algorithms, Applications by Meinard Müller, the coefficients $d_\omega$ and $\phi_\omega$ are defined as
where $\cos_{\omega,\phi}(t) = \...
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486
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Solve Efficiently the 1D Total Variation Regularized Least Squares Problem (Denoising / Deblurring)
How to solve a 1D Least Squares with Total Variation Regularization?
I know gradient based methods, I wonder how much faster / efficient I can get.
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148
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Converting Hadamard Product into Matrix Multiplication in Image Deconvolution with Total Variation (TV) Using ADMM
I would like to solve the following Image Deconvolution equation by ADMM.
$$\mathbf { \min\frac{1}{2}\Vert{Cx-b}\Vert_2^2+\Vert w\circ (D x)\Vert_1 \tag 1}$$
Where, $x$ is a vector of unknown pixel ...
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2
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Generate the Matrix Form of 1D Convolution Kernel
As a follow up to Generate the Matrix Form of 2D Convolution Kernel, could someone explain how to generate the matrix form of a 1D convolution kernel?
How different convolutions shapes are handled?
...
- 357
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2
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387
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Projection Matrix derivation to constrained optimization problem with Lagrange multiplier
I am trying to derive famous Projection operator as a constrained minimization problem for the least square problem. The question is as follows:
Find $x$ minimizing $ (y-x)^T(y-x)$ subject to $x = H\...
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338
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Tikhonov Regularization for Complex Matrices
Tikhonov regularization is used to regularize ill-posed inverse problems if the matrix $A \in \mathbb{R}^{n,m}$ to be inversed has a high condition number. For example
$$
A=\begin{bmatrix}1&1\\
1&...
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How to update point spread function of blind deconbolution by conjugate gradient?
There is an unblurred image $g$ and a blurred image $x$.
Their relationship is expressed by the following formula using $psf$(point spread fucntion, size is $5×5$ kernel).
$g = x \otimes psf\tag 1$
...
4
votes
1
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183
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How to Solve the Image Dehazing Problem Using ADMM?
I want to solve the image dehazing problem using ADMM.
I want to use the proximal algorithm to optimize each element.
I refer to this treatise: Efficient image dehazing with boundary constraint and ...
0
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1
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265
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How to Solve Blind Image Deblurring with Total Variation (TV) Prior Using ADMM?
As a continuation of the question How to Solve Non Blind Image Deblurring with Total Variation Prior Using ADMM? I would like to understand how could one solve the Blind Deblurring (Deconvolution) ...
- 357
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Optimization of square matrix multiplied with another matrix to have the final result a unitary matrix
I have a square matrix $D$ whose size is $m \times m$ multiplied with another $m \times m$ square matrix $C$, I need to optimize the matrix $C$ to have a unitary matrix $DC$. I mean optimize the ...
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How to Solve an Image Deblurring Problem by Variational Methods Using ADMM?
Following up on a previous question, I wanted to understand how to solve an image deblurring problem using Variational methods in matlab or julia.
Given some original blurry image $f$, I would like to ...
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How to Solve Non Blind Image Deblurring with Total Variation Prior Using ADMM?
How could one use the Total Variation frame work to solve the Deblurring problem?
Specifically using the ADMM as a solver.
One could assume the blurring operator is known, linear and shift invariant.
...
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How to Solve Image Denoising with Total Variation Prior Using ADMM?
I was looking at some articles or Wikipedia on denoising images using the Total Variation norm. The setup is the Rudin Osher Fatemi (ROF) scheme, and the corresponding equation is:
$$
F(u)=\int_{\...
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Why Does the Median Filter Minimize the Absolute Value Error $L_1$ Cost Function?
I can easily prove that the mean filter minimizes the square error $L_2$ cost function using simple calculus.
However, how do you prove that the median filter is optimal with respect the absolute ...
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time-domain channel estimation based on two vectors optimization
Let's the input data vector $X = [X_1, X_2, X_3, X_4, X_5,X_6,X_7,X_8];$ where $[X_7,X_8]$ are well known, and the vector $y = h*X$ where $*$ is the convolution operation and $h = [h_1,h_2]$ is the ...
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Super Resolution in Frequency Domain Using Compressed Sensing
To be noted that I'm very new to this topic, I would like to understand the fundamentals of how to get Super Resolution in Frequency Domain estimation using the Compressed Sensing Model.
I am also ...
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Compressed Sensing in DOA processing
I'm trying to apply the compressed sensing theory (CoSaMP algorithm) to the DOA estimation in FMCW ULA (made of 48 elements). In the dechirped signals processing I use a first FFT to solve the range ...
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Is Sum of Absolute Value / $ {L}_{1} $ Norm of Differences Convex?
I'm not sure how to approach this exercise.
One idea is to derive it w.r.t z, show that there is a min-extremum at $z=f_k$ and then show that for each value from the right and the left of the loss ...
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51
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Transform a data set by exploting the vectorfield
I am somewhat new in the field of Digital Signal Processing / Image processing.
As shown in the figure, I have 4 straight lines $f_i(x)$ with $i = 1,\dots, 4$ that pass through $g(x)$. Similiarly ...
3
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1
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101
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Minimize the Cost Function of Values of Vectors Based on Their Amplitude
I have two vectors $X = [x_1,x_2,x_3,x_4]$; and $Y = [y_1,y_2,y_3,y_4]$; I know that $|x_1|$ = $|y_1|$, and $|x_2|$ = $|y_2|$,... so on. it means the difference is only in the sign. it might be ...
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