Questions tagged [optimization]

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1answer
38 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 ...
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1answer
48 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 ...
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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{...
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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 ...
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1answer
31 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 ...
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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 ...
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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 ...
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2answers
63 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 ...
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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 ...
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1answer
50 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 ...
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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 + \...
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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 $ ...
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1answer
40 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 \...
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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 ...
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1answer
47 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 ...
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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 ω, c1, c2, r1 and ...
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1answer
51 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 ...
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2answers
120 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 ...
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0answers
25 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 ...
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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 ...
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1answer
58 views
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2answers
173 views

Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm [closed]

How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
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1answer
87 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 ...
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1answer
50 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 ...
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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. ...
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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 ...
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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} = \...
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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 ...
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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 ...
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2answers
151 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 ...
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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 ...
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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 ...
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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: <...
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2answers
87 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 ...
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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 ...
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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
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0answers
134 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, ...
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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
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1answer
108 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
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1answer
194 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 ...
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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
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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
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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
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1answer
87 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 ...
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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::...
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1answer
94 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
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2answers
99 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 ...
1
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1answer
135 views

IMU Speed Tracking Through Known Path

I am new to signal processing and Kalman Filtering here. Thanks for your help. I working with an IMU for a tracking project where the IMU moves throw a known path but at an unknown speed (within ...
1
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2answers
720 views

Why Is Non Linear Least Squares Method from MATLAB and Alglib Gives Different Results on the Same Data?

i'm trying to rewrite my Matalab prototype for some DSP to C++ and encountering a displeasing problem. I'm trying to fit data to a function $y = a * (\pi / 2 + arctg(b * x))$. In Matlab it works well ...
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0answers
46 views

Optimization of a continuous function

This is more like an optimization problem but any solution is appreciated. I have a data set with input specifying power(demand) to be generated for a particular time period(TP). Input: Time --- ...