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Questions tagged [optimization]

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0
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2answers
64 views

Subgradient Method for K-Means Like Problem

I want to solve k-means-like problem. But at first, I wonder that we can apply subgradient method to k-means problem. We want to find the optimal clustering $S = (S_1,S_2,...,S_k)$ such that $$ {\...
2
votes
1answer
446 views

What Is the Difference between RLS, LMS and Wiener Filter? When Is One Preferred Over Another?

I'm dealing with a channel equalization problem where the channel is modeled as a WSS process. I understand LMS utilises a Wiener-like approach, ie it converges to the optimal (wiener) solution. I ...
1
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1answer
96 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,\...
0
votes
1answer
74 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 ...
10
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0answers
592 views

Will an Unscented Kalman Filter Be “As Good” as Other Optimization Algorithms for This Problem?

I want to calibrate a tri-axis magnetometer when a tri-axis gyroscope is also available. I am fairly certain I can solve this problem using various optimisation algorithms, but I would prefer to use ...
5
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0answers
554 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 ...
3
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0answers
90 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
votes
0answers
67 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 ...
3
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0answers
114 views

Signal reconstruction in compressed sensing with a simple vector signal as an example

While going through the different types of reconstruction algorithm as mentioned in lecture notes in Compressed Sensing by Richard G. Baraniuk, I came to know that minimum $l_1$ norm reconstruction is ...
3
votes
0answers
74 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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0answers
155 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
103 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
29 views

Optimization Problem Involving Frobenious Norm, Linear Equality Constraints and Semi Orthogonal Matrix

I have a question, Suppose $ A, B, D \in \mathbb{R}^{n \times p} $, I want to solve the following optimization problem: $\arg\min_D\frac{1}{2}\|D + A\|_F^2 + \lambda\|BB^T + DB^T + BD^T\|_1 \mbox{ s....
1
vote
0answers
19 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
41 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
136 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
132 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
383 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
89 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 ...
1
vote
0answers
296 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 ...
1
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0answers
137 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,...
0
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0answers
44 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
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0answers
19 views

Linear equation set construction for Brox et al. optical flow optimization

I'm trying to implement an optical flow calculation program for two successive images based on this article by Brox et al. The Euler-Lagrange combined with a fixed point iteration loop yields two ...
0
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0answers
20 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 ...
0
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0answers
35 views

How to normalise data for iterative computation of extrinsic camera matrix?

Hartley & Zisserman defend that data normalisation is an essential step prior to the estimation of geometric image transformations. The reasoning behind this, as stated in their book [1, Section 4....
0
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0answers
40 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
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0answers
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 ...
0
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0answers
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 $y\in \mathbb{R}^m$ ...
0
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0answers
714 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,...