Questions tagged [optimization]
The optimization tag has no usage guidance.
143
questions
0
votes
1answer
11 views
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{...
-1
votes
1answer
47 views
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?
0
votes
0answers
31 views
Find similarities between 2 signals
Is there any heuristic method to find metrics, similarities between two signals?
I am not talking about correlation.
0
votes
0answers
19 views
Iterative beamforming IB
Is iterative beamforming (IB) an algorithm on its own, or is it an extension of the EM algorithm, how does IB differ from the latter, knowing that EM iterate 2 steps (the E step and the M step) and so ...
0
votes
0answers
11 views
How to create an objective function for Mackey glass time series (using "bayesopt")?
I am optimizing 5 hyperparameters of Mackey-Glass time series and using built-in function "bayesopt" in MATLAB. My Mackey glass time series with fixed parameters shows correct results. ...
4
votes
1answer
53 views
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 $$\mathbf{A}\mathbf{x} = \...
1
vote
1answer
52 views
Why an does an integrate-and-dump stage in a CIC filter provide the same functionality as the integrator and comb in series?
I have a hard time understanding why the combination of integrator and comb (integrate-and-dump) is the same as a separate integrator and comb in series like in this picture:
Please explain why these ...
0
votes
0answers
27 views
Modern method for feature Gaussianization
Suppose non-negative feature vectors $X = [x_0, x_1, ..., x_{N-1}]$. Existing methods include:
BoxCox
Lambert
Iterative, rotations
Log-median:
$$
\hat X[n, p] = \log \left(1 + \frac{X[n, p]}{C \mu[p]...
3
votes
1answer
56 views
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 ...
2
votes
1answer
87 views
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) = \...
6
votes
1answer
101 views
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.
0
votes
0answers
118 views
Space-Time Finite Element and Static Condensation for Sensor Fusion
My recent pastime interest deals with the nonlinear sensor fusion of GNSS, barometer, magnetometer, accelerometer and gyroscope data. I had a look at the EKF, UKF and Particle Filters but gave up as ...
4
votes
1answer
64 views
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 ...
4
votes
2answers
673 views
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?
...
1
vote
2answers
145 views
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\...
4
votes
1answer
128 views
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&...
0
votes
0answers
37 views
Multi-objective Shortest Path Problem
I am attempting to solve a shortest-path algorithm with Dijkstra. However, I have multiple cost functions. I am eager to combine these costs. What is the best and most accepted way of doing this ...
1
vote
0answers
84 views
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$
...
0
votes
0answers
9 views
Why are different methods used to optimize energy function for optical flow and stereo vision?
Optical flow and stereo vision both try to estimate dense correspondence from each pixel in one image to matching pixel in another image.
For optical flow, the two images are taken from the same ...
4
votes
1answer
130 views
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 ...
3
votes
1answer
85 views
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) ...
1
vote
2answers
103 views
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 ...
4
votes
1answer
69 views
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 ...
5
votes
1answer
110 views
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.
...
6
votes
2answers
271 views
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_{\...
0
votes
0answers
19 views
Optimal control to maximize the ratio between two systems
I have two (or more) systems with analytic (but somewhat big and unwieldy) step responses $H_1(t)$ and $H_2(t)$ both of the same form (eq. A6a onwards in https://doi.org/10.1016/S0302-4598(97)00093-7),...
6
votes
1answer
89 views
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 ...
0
votes
1answer
60 views
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 ...
5
votes
1answer
213 views
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 ...
2
votes
0answers
66 views
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 ...
4
votes
1answer
77 views
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 ...
0
votes
1answer
48 views
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
votes
1answer
71 views
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 ...
1
vote
1answer
43 views
Optimization of harmonics calculation
I need to compute the sine and cosine of an argument along with n "harmonics"
\begin{matrix} \sin(x) & \cos(x) \\
\sin(2x) & \cos(2x) \\
\cdots \\
\sin(nx) & \cos(nx)
\end{...
0
votes
3answers
128 views
Compute Hann window without cos function
In an environment with limited memory and computing power it is interesting to be able to generate a Hann window without using a cache or repetitive calling of expensive functions such as sine and ...
1
vote
1answer
49 views
How to find the value of regularization parameter/s when having one or multiple priors
I am working on a image reconstruction framework, specifically interferometry. In simple words we have data that is pertubated by noise, say
$$
V^o_i = V_i + \sigma_i
$$
Where $V^o$ is a complex ...
0
votes
1answer
28 views
How can I infer the cost function from Kruppa's simplified equations
The following equations are Kruppa's simplified equations used in camera autocalibration. My objective here is to infer the cost function(Error Function) from this equations, So I can minimize the ...
5
votes
2answers
149 views
Quadratic Programming with Linear Equality Constraints
I need to solve an equality constrained minimization problem as give below
$$\min_{\textbf{w}} \mathbf{w}^TR\mathbf{w} $$
such that
$$X\mathbf{w} = \mathbf{1}$$
where $R\in \mathbb{R}^{n\times n}$ is ...
0
votes
1answer
104 views
Sparse recovery, Restricted Isometry Property for ILL-POSED problems
if $\mathbf x$ is $N\times 1$ sparse vector, and $\mathbf A$ is an $M\times N$ matrix with $M<<N$, and we measure $\mathbf y=\mathbf{Ax}$, then compressed sensing theory tells us that we can ...
0
votes
0answers
24 views
Maximizing sum-rate with constraints
I have an SNR measure, which is a ratio of two linear functions, and I need to maximize the sum rate of a cellular system given by
$$R = \sum_{i=1}^{N_{1}}\sum_{j=1}^{N_{2}}\mathrm{log}_{2}\left(1 + \...
1
vote
0answers
26 views
Image Restoration and Standard Forms of Second Order Cone Programming (SOCP)
I'm studying the application of SOCP methods in Image restoration And I want to understand the difference between the two formulas of SOCP and how they are related.
Standard form (1) :
min $f^{t}x $
...
4
votes
1answer
148 views
Solving LASSO (Basis Pursuit Denoising Form) with LARS
I'm now working on using LARS (Least Angle Regression) algorithm to solve a LASSO problem in Basis Pursuit Denoising form like:
\begin{align*}
\quad && \arg \min_{\beta}{\left\| y - X\beta \...
5
votes
1answer
133 views
On the Measurement Matrix Used for Compressing Sensing
Assume we have a matrix $x$ of size $(8,8)$ where each column is considered to be sparse with degree of sparsity equals to $4$. it means that every column can have $4$ zeros and $4$ non-zeros values ...
0
votes
1answer
83 views
On the Use of OMP Algorithm to Estimate Sparse Vector
As known, Orthogonal Matching Pursuit (OMP) Algorithm is to recover the sparse channel after convolution with another vector. But when I implement that in MATLAB, I don't get the sparse vector ...
2
votes
1answer
91 views
Minimizing Time Sidelobes with Pulse Compression
I am trying to compute a compression filter function to minimize the error from a a desired pulse compression result.
The usual approach to doing this is to minimize the RMS error of the the ...
4
votes
2answers
220 views
Proximal Gradient Method (PGM) for a Function Model with More than 2 Functions (Sum of Functions)
I am currently working in signal reconstruction. I am trying to develop an algorithm where the user can plug any constraint to the main objective function (let's say chi2, least squares). I was trying ...
1
vote
0answers
27 views
Rakeness Optimization problem
Rakeness optimization problem demonstrate that increases the rakeness between a , b while leaving b random enough.
where e is the energy of the projection waveforms and r is a randomness-enforcing ...
0
votes
0answers
31 views
non-uniform antenna array design
There are tons of papers discussed this topics and most of them are related to fancy optimization techniques (convex/non-convex). I am wondering if we can have a simpler way to find the antenna ...
4
votes
1answer
82 views
Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm - Fix Given Code [closed]
This is my implementation which doesn't work:
...
2
votes
2answers
300 views
Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm [closed]
How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?