Questions tagged [optimization]
The optimization tag has no usage guidance.
118
questions
0
votes
0answers
25 views
decomposition of a function to piecewise functions
Is the next answer correct:
$$a\left(z\right)=\sum _{\left\{k\right\}U\left\{k'\right\}:f_k\le \:z,\:z\:\in R,\:f_{k'}\ge z\:;\:z\ge 0}1-\frac{f_k}{z},\:b\left(z\right)=\sum _{\left\{k\right\}:f_k>...
1
vote
1answer
48 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
0answers
26 views
sampling using L1 optimization
As much as I understand the F should be the interval medians (correct me if I wrong), according to the next slide, where is also the Loss function defined:
What I don't understand is the next note in ...
0
votes
1answer
40 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 ...
1
vote
1answer
51 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
42 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
115 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 ...
0
votes
1answer
35 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
$$
Where $V^o$ is a complex ...
0
votes
0answers
18 views
Can I use a filter design to optimize the preconditioning of an optimizer?
Consider a noisy time series y_i and that I have waited until end of experiment. I now want to fit a nonlinear parameterized function F(A,d,k; t) to determine A,d,k.
So I can happily Newton-Raphson ...
0
votes
1answer
24 views
How can I infer the cost function from Kruppa's simplified equations
The following equations are Kruppa's simplified equations used in camera autocalibration. My objective here is to infer the cost function(Error Function) from this equations, So I can minimize the ...
3
votes
2answers
67 views
Quadratic Programming with Linear Equality Constraints
I need to solve an equality constrained minimization problem as give below
$$\min_{\textbf{w}} \mathbf{w}^TR\mathbf{w} $$
such that
$$X\mathbf{w} = \mathbf{1}$$
where $R\in \mathbb{R}^{n\times n}$ is ...
0
votes
0answers
19 views
Basis pursuit denoising for complex valued data
Basis pursuit denoising is given in the form
$$\min_{x}{\frac {1}{2}}\|y-Ax\|_{2}^{2}+\lambda \|x\|_{1}$$
It is repeated in literature that when $y$, $A$, and (possibly) $x$ are complex valued, the ...
0
votes
1answer
54 views
Sparse recovery, Restricted Isometry Property for ILL-POSED problems
if $\mathbf x$ is $N\times 1$ sparse vector, and $\mathbf A$ is an $M\times N$ matrix with $M<<N$, and we measure $\mathbf y=\mathbf{Ax}$, then compressed sensing theory tells us that we can ...
0
votes
0answers
23 views
Maximizing sum-rate with constraints
I have an SNR measure, which is a ratio of two linear functions, and I need to maximize the sum rate of a cellular system given by
$$R = \sum_{i=1}^{N_{1}}\sum_{j=1}^{N_{2}}\mathrm{log}_{2}\left(1 + \...
1
vote
0answers
22 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 $
...
2
votes
1answer
47 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
106 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
50 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 ...
0
votes
0answers
6 views
Neural network SOM vs PSO ( Maybe like neuron swarm total fitness optimization !!!)
I ave seen the Neural network SOM equations like this:
and this PSO equation:
Where xBest and gBest denote the best particle position and best group
position and the parameters Ļ, c1, c2, r1 and ...
2
votes
1answer
52 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 ...
3
votes
2answers
126 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
26 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
28 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 ...
2
votes
1answer
60 views
Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm - Fix Given Code [closed]
This is my implementation which doesn't work:
...
0
votes
2answers
178 views
Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm [closed]
How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
3
votes
1answer
88 views
Convex Optimization with $ {L}_{1, 2} $ Regularization Term
I have an optimization problem such as follow:
$$\underset{X}{\operatorname{argmin}}\sum _s \left \| T_sX_{:,s} - Y_{:,s} \right \|^2_2 +\lambda\left \| GX \right \|_{2,1} \tag{1}$$
I have introduced ...
1
vote
1answer
54 views
Resources on Solving Convex Optimization Problems in the Compress Sensing Field
When I read papers of compressed sensing, sparse representation and whatever requiring optimization of a cost function, I just find the final results as an iterative equation or so which will converge ...
1
vote
0answers
103 views
Sparse Bayesian Learning Algorithm in Python - MSE vs. SNR
I am implementing SBL in python. I have plotted a graph between MSE (mean squared error) and SNR (Signal to Noise ratio)
The graph must be decreasing, but mine is decreasing till the SNR is negative. ...
1
vote
1answer
35 views
Why does it seem most of people will optimize the downlink rate,not the uplink rate?
I search for some papers about energy harvest,SWIPT and optimization.And i found that there is just one paper to optimize the uplink rate,the others are for optimizing the harvested power,power budget ...
0
votes
0answers
99 views
On the transmit weight vector in MIMO-MRC systems
Recently, I am reading paper [1]. In this paper, the author wrote:
In MIMO-MRC systems in the absence of interferers, the signal vector at the received $n_R$ antennas is given by
$$\mathbf{r} = \...
0
votes
1answer
77 views
Efficient correlation of a low duty cycle training sequence
Is there a way to efficiently correlate a training sequence that is N samples long, framed at M samples where M >> N, with L occurrences of such frames (see below). For the pedants, the training ...
1
vote
0answers
30 views
Bundle adjustment optimization parameters
While reading the Wikipedia article on Bundle adjustment, I came across the following objective function used to represent the bundle adjustment problem.
I have two questions regarding this objective ...
2
votes
2answers
166 views
Constrained LASSO Problem - $ {L}_{1} $ Regularized Least Squares with Linear Equality Constraints
I have an optimization question.
I want to solve the following problem:
$$
\arg\min_S\frac{1}{2}\|s-c\|_2^2 +\lambda\|\Phi s\|_1 \mbox{ s.t. } As = 0
$$
in which $\Phi$ is the wavelet transform ...
1
vote
0answers
60 views
Optimal sensor placement for 3D TDoA positioning
Suppose there is a rectangle indoor area, we want to locate different positions within this area using TDoA estimations. 5 sensors are placed to obtain optimal 3D positions with TDoA errors, we only ...
0
votes
1answer
73 views
Promote the Orthogonality between Rows of $ S $
I have a question.
Suppose we want to solve an optimization problem:
Consider $S \in \mathbb{R}^{N \times T}, T >> S$
$$\min_{S} f(S) \mbox{ s.t. } SS^T \mbox{is diagonal}$$
Which means each ...
0
votes
2answers
86 views
How do you properly organize data to compute multiple (independent) recursive filters at the same time taking advantage of SIMD instructions?
I'm processing multiple (independent) Exponential Moving Average 1-Pole filters on different parameters I have within my Audio application, with the intent of smooth each param value at audio rate:
<...
1
vote
2answers
88 views
How to efficiently control an FIR's magnitude response by altering its phase spectrum
Question:
Extensively searching the space of all possible vectors of length $n$ to satisfy a (non-overdetermined) requirement is possible in principle. Hence, there is a way to calculate a complex ...
0
votes
1answer
52 views
Wireless Body Area Networks with Minimum Energy Consumption [closed]
For adaptive compressive sensing(cs),the sensing matrix is related to the input signal.
For example, in rakeness-based(cs), the sensing matrix is obtained by solving an optimization problem which ...
0
votes
2answers
57 views
Control optimization problem
I am running into a problem where I have a control system $S[t]$ that takes a control $C[t]$, so that
$$S[t+1] = H(C[t,t-1,...], S[t,t-1,...])$$ the response of the system is the history of controls ...
3
votes
0answers
135 views
How to implement the RLS for matrices
I need to implement the RLS algorithm but it's for matrices instead for vectors, I have made the below code, but still something wrong is not working well,
EDIT:
The code should be done as below,
...
1
vote
0answers
23 views
Improve NMF for data with partial overlaps in multiple groups?
I want to use NMF to separate true sources from data. My data is in group structure with overlap elements. For example (in the smaller version)
group1: contains A,B,C,D,E,F,G patterns
group2: ...
3
votes
1answer
109 views
How Is Mixed Norm ($ {L}_{1, 2 }$) Better than $ {L}_{1} $ Norm for Sparse Representation?
Using $ {l}_{1} $-norm regularization for the purpose of achieving sparsity of the solution has been successfully applied a lot. But many times, I found the paper using mixed-norm instead of $l_1$-...
3
votes
1answer
203 views
How to Formulate a Constraint Which Ensures All Variables Have the Same Sign
I'm trying to include a constraint in my problem (to be solved by any convex optimization solver). Let {a,b,c,d ...} be a finite set of continuous variables. How to formulate a constraint which ensure ...
4
votes
0answers
69 views
Designing a fast linear operator with $\pm 1$ entries with low condition number and low Hamming distance between consecutive rows
I need to design a matrix for compressive imaging where each row represents an $N$-pixel filter in a focal plane through which light is masked, summed, and measured (think of Rice's single-pixel ...
4
votes
3answers
4k views
Derivative with respect to complex conjugate
I have a real function $C$ of a complex vector $x$. While taking the gradient of the function $C$ for minimising the same, why do we take the derivatives with respect to the complex conjugate of $x$, ...
2
votes
1answer
146 views
Sequential Non Linear Least Squares Problem
I have the the following non-linear function,
$$s(x;A_k,\mu_k,\sigma_k)=\sum_{k=1}^2 A_k \exp\left(\frac{-(x-\mu_k)^2}{\sigma_k^2}\right)$$
with unknown (but deterministic) parameters $A_k,\mu_k,\...
2
votes
1answer
90 views
Sparse Recovery Best Algorithms
In the big data era, in order to control the cost, complexity, and bandwidth of collecting and processing high-dimensional data systems, it is critical to exploit models that ...
1
vote
2answers
3k views
Fastest Available Algorithm to Blur an Image (Low Pass Filter)
Iam working with a camera that produces ugly artifacts:
by using ANY blur filter on the camera's output the visual quality improves drastically:
The above image was created using OpenCV's cv::...
1
vote
1answer
98 views
The Gradient Operator of a Vectorized Image in Matrix Form
I have this optimization problem:
$$ \arg \min_{ X \left( i, j \right) } \sum_{i, j} \left\| X \left( i, j \right) - 255 \right\|_{2}^{2} + \lambda \sum_{i, j} \left\| \nabla X \left( i, j \right) - \...
3
votes
2answers
100 views
Orthonormal Dictionaries for Band Limited Signals
If $\mathbf{x} = [x_0, x_1, \ldots, x_{N-1}]^T$ is the time sampled input signal and $\mathbf{Y} = [Y_0, Y_1, \ldots, Y_{N-1}]^T$ is the Fourier transform of the input signal, then a linear ...
