Questions tagged [optimization]

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600 views

fit theoretical spectrum to simulated one

I have a bunch of simulated time series, for which I can compute the power spectrum. Generally, the simulated power spectrum can be sketched as follows: I now aim to calculate the features of the ...
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70 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 ...
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148 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, ...
3
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0answers
77 views

When Does $ {L}_{1} $ Regularization Give a Sparse Solution?

I was maximising a likelihood function, which is convex. I know that the system has a K-sparse solution. I wanted to know the conditions (or some sufficient conditions) on the likelihood function ...
2
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62 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 ...
2
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0answers
170 views

Any idea how can I optimize morlet wavelet parameters by Heisenberg uncertainty principal and Shannon entropy?

Based on a paper in here, they have proposed a method to optimize morlet function parameter. I have tried to implement their technique, but I can't get rational results. any idea? In here you can see ...
2
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0answers
110 views

Phong Reflection Model Parameters

Question: Can anyone refer me the Phong reflection model parameters for a face image taken for web-cam? Details: I am doing 3D reconstruction of 2D images using 3D Morphable Model as in this paper ...
1
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0answers
82 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). $g = x \otimes psf\tag 1$ ...
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24 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 $ ...
1
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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 ...
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126 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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34 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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64 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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0answers
24 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: ...
1
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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 --- ...
1
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0answers
160 views

Pattern recognition

I am new to the world of computer vision, so please excuse my basic questions. I have two patterns: one consisting of a single circle of radius $r$, and one made of several circles, still of radius $...
1
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0answers
220 views

Converting a parallel filterbank to cascade structure

I have a bank of 12 bandpass filters (biquads) that I use for spectral modelling. Each filter is centered around a specific "mode" frequency, and has its own resonance. Until now I have implemeted ...
1
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0answers
459 views

Finding lag times for multiple time series

I have $N$ time series which have unknown time offsets relative to each other. I want to estimate the $(N - 1)$ time offsets, $\tau_{i,i+1}$, which maximise the sum of the cross-correlations between ...
1
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0answers
141 views

How to Avoid Perspective Distortion Buildup in a Planar Mosaic

Registering images for map or other planar mosaic from a handheld camera or a drone requires projective transform (homography) as the camera is allowed to rotate between frames. Unfortunately, planar ...
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0answers
388 views

Biquad Filter Optimization

I would like to try optimize a bit more the biquad filters indended for RIAA/non-RIAA equalization at low samplerates (44.1/48kHz). Are there any open source optimization libraries (C, C++ or C#) out ...
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149 views

Optimal filter bank from SVD/PCA

Given a million data points in say 100d, is there a way to generate an optimal filter bank of say 20 filters from an SVD of the data ? Call the 100d space $F$ (as in Frequency), with coordinates $[f_1,...
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26 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]...
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117 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 ...
0
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35 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 ...
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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 ...
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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),...
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62 views

Optimal sampling rate for the HMM forward-algorithm

I have a system with a binary-state. The system state is estimated by an HMM forward-algorithm. Also, the system allows a varying sampling rate. Considering that the system state transition takes a ...
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22 views

how to do initialization of random vectors in matlab

I have to generate random vectors for $\mathbf{p}^{(0)}$, $\mathbf{u}_l^{(0)}$, and $\mathbf{v}_l^{(0)}$ for $l=1\ldots L$. Now I am confused about how to generate these vectors as $l=1\ldots L$ is ...
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28 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>...
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30 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 ...
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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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29 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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0answers
118 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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33 views

Frequency identification as a convex problem

Suppose I have two time series, $x(t)$ and $y(t)$: $x$ is the output of a sine wave generator, and $y$ is the generator's frequency setting. Given a training set of $(x, y)$ pairs, Is it possible to ...
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24 views

How to decide about length of vectors for estimating correlation matrices

I am optimizing a filter $f$ using mean squared error criterion. $$MSE = f^T*(R_{xx}-R_{yx}^T*R_{yy}^{-1}*R_{yx})*f \tag{1}$$ where $x\in \mathbb{R}^n$ input column vector $y\in \mathbb{R}^m$ ...
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721 views

Digital Image Processing - Contemporary Research Topics

I need to propose a masters degree topic, and I'd like it to be in digital image processing. What are currently relevant topics in this area? I suppose that I'm looking for some kind of optimization,...