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Need help with deriving a recursive formula for a control system optimization integral

I need some help with a problem that appears in one of the exercises of "Introduction to Stochastic Control Theory" by Karl J. Åström: Chapter 5, page 141, problem 8. It is about deriving a ...
mattTheMathLearner's user avatar
1 vote
1 answer
37 views

Tune Least Squares Support Vector Machine (LS-SVM) With Grid Search Optimization

I am looking for LSSVM with Gride Search optimization in Python, but could not find it. Scikit learn has SVM with Grid Search but not for LSSVM.
novin's user avatar
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1 vote
1 answer
74 views

Deriving the posterior distribution parameters of a normal distribution in the context of dereverberation

Context: $\bar{\Theta}$ is the room regression filter coefficients (RRC); $$X_{t} = \bar{\Theta}^{H}\bar{X}_{t-1} + s_{t}$$ means in words: the filter that defines how the room causes reverberation to ...
user3371266's user avatar
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1 answer
30 views

How to select the location of submatrices to have specific property in the output of multiplication

I want to set the locations of two submatrices W22 and W21 taken from Hadamard matrix, with respect to ...
Sajjad's user avatar
  • 167
2 votes
2 answers
76 views

Fit Data Samples with a Robust Fit

I have a data from a sensor which the connection model of $x$ and $y$ is known: For instance, in the case above, the model is linear. The issue is how to handle outliers. Specifically when there are ...
Royi's user avatar
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1 vote
1 answer
92 views

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\...
Fatima_Ali's user avatar
2 votes
1 answer
64 views

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 ...
Omri's user avatar
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43 views

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 ...
Yair M's user avatar
  • 305
1 vote
1 answer
102 views

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?
Srikanth's user avatar
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0 answers
81 views

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 ...
aybe's user avatar
  • 284
4 votes
1 answer
166 views

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 ...
Adam S.'s user avatar
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4 votes
1 answer
341 views

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}...
MaxFrost's user avatar
  • 383
2 votes
1 answer
157 views

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}_{{ \...
Hadeel's user avatar
  • 83
3 votes
1 answer
125 views

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 ...
mlbj's user avatar
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3 votes
0 answers
67 views

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 ...
Sajjad's user avatar
  • 167
1 vote
1 answer
99 views

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 ...
yourds's user avatar
  • 123
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1 answer
151 views

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 ...
c1119's user avatar
  • 41
1 vote
0 answers
52 views

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 ...
Giray Salgır's user avatar
1 vote
0 answers
35 views

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, ...
10GeV's user avatar
  • 123
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1 answer
505 views

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 ...
CVDE's user avatar
  • 103
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1 answer
53 views

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 ...
budding_scholar's user avatar
1 vote
2 answers
186 views

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, ...
arb01234's user avatar
2 votes
0 answers
45 views

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 {\...
bla's user avatar
  • 588
6 votes
2 answers
435 views

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 ...
Gillespie's user avatar
  • 1,906
0 votes
1 answer
61 views

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)...
chaaru's user avatar
  • 37
0 votes
1 answer
45 views

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 ...
Creator's user avatar
  • 108
2 votes
2 answers
186 views

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 ...
papaya's user avatar
  • 43
2 votes
0 answers
156 views

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 ...
Name123's user avatar
  • 23
3 votes
2 answers
375 views

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 ...
JXuan's user avatar
  • 55
0 votes
1 answer
67 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{...
Riva11's user avatar
  • 5
-1 votes
1 answer
69 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?
Blobmou's user avatar
  • 59
0 votes
0 answers
62 views

Find similarities between 2 signals

Is there any heuristic method to find metrics, similarities between two signals? I am not talking about correlation.
Blobmou's user avatar
  • 59
4 votes
1 answer
104 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} = \...
bla's user avatar
  • 588
1 vote
1 answer
439 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 ...
Yegor Krapovnitskyi's user avatar
0 votes
1 answer
190 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 ...
Mark's user avatar
  • 367
2 votes
1 answer
263 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) = \...
S.H.W's user avatar
  • 726
2 votes
1 answer
659 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.
Mark's user avatar
  • 367
4 votes
1 answer
167 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 ...
Sushi man in Japan's user avatar
1 vote
2 answers
3k 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? ...
Mark's user avatar
  • 367
1 vote
2 answers
469 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\...
Osman Coskun's user avatar
4 votes
1 answer
398 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&...
Bulbasaur's user avatar
  • 209
1 vote
0 answers
95 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). $g = x \otimes psf\tag 1$ ...
Sushi man in Japan's user avatar
4 votes
1 answer
186 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 ...
Sushi man in Japan's user avatar
0 votes
1 answer
294 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) ...
Mark's user avatar
  • 367
1 vote
2 answers
150 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 ...
Fatima_Ali's user avatar
4 votes
1 answer
501 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 ...
krishnab's user avatar
  • 257
2 votes
1 answer
328 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. ...
Mark's user avatar
  • 367
6 votes
2 answers
2k 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_{\...
krishnab's user avatar
  • 257
6 votes
1 answer
193 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 ...
Izzo's user avatar
  • 882
0 votes
1 answer
77 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 ...
Fatima_Ali's user avatar