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Questions tagged [optimization]

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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
62 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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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 ...
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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 ...
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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....
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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 ...
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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....
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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 ...
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1answer
66 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
48 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
79 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
46 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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1answer
43 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 ...
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88 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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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: ...
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1answer
74 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 $l_1$-...
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1answer
31 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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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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3answers
545 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 $x$, ...
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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,\...
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1answer
68 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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1answer
567 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
49 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) - \...
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1answer
116 views

Automatic Image Enhancement of Images of Scanned Documents (Auto Whitening)

Dropbox have make a blog post about there automatic enhancement method for scanned document image - Fast Document Rectification and Enhancement. I followed the post and they mention a formula to make ...
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2answers
77 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 ...
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1answer
91 views

IMU speed tracking through known path

new to signal processing and KFiltering 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 limits), the ...
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2answers
337 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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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 --- ...
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2answers
91 views

Solving LASSO ($ {L}_{1} $ Regularized Least Squares) with Gradient Descent

To the best of my knowledge, state of the art methods for optimizing the LASSO objective function include the LARS algorithm and proximal gradient methods. I was wondering however, if the LASSO ...
0
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1answer
58 views

Optimal segment length for coherence estimation

I have a question about the computation of coherence between two signals with Welch's method. The two signals are relatively short (e.g. 256 samples) and I would like as correct an estimate of shared ...
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135 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 $...
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1answer
60 views

Optimization‏ FIR filter

I have a doubt about this : Iterative methods for optimization‏ in FIR filter (on the one hand traditional like window,frequency sampling ,WLS,Remez Exchange...,on the other hand evolutionary methods ...
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2answers
366 views

Why Do Most of The Papers Use the Frobenius Norm for Denoising?

I have an noisy image and I want to remove noise from it; suppose $y$ is noisy image and $A$ is linear mask which makes my image noisy and $x$ is original image, so we have $$ Ax + \eta = y $$ and $\...
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2answers
75 views

Why use parametric based estimation methods - confusion regarding terms

Using the probability density function (pdf) we can estimate an unknown parameter using methods such as Maximum Likelihood estimation. If the pdf is not available, then Least Squares can be used. ...
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2answers
319 views

Reference Code for Positive Basis Pursuit Denoising

I am trying to reconstruct a positive sparse signal using compressed sensing (friedlanders code), I cannot find a way to impose the positivity constraint for this implementation. I have seen some ...
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1answer
120 views

Properties of Optimization Techniques in Filter Design

I have this design: Can you tell me about the type of filter and the algorithm just viewing this design, or should there be other information?
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1answer
285 views

How to Use the DFT (FFT) to Solve a Least Squares Regularization Problem (Inverse Problem)?

Let $X$ and $K$ be an image and a Point Spread Function (PSF), respectively. The blur image $B$ is obtained as follows $$B = X * K$$ I want to solve the following general regularization problem $$...
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130 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 ...
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1answer
75 views

MATLAB optimization for a subroutine function

I am going to find the optimum values for a subroutine function in MATLAB. the subroutine function is not accessible in a mathematical form and we don't know any thing about it. We have ten input ...
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2answers
228 views

Best Metric to Compare Sparsity of Vectors

I solved the Basis Pursuit Denoising Problem looking for a sparse solution (I am in compressive sensing): $$ x^* = \text{arg min}_x \left\{\frac{1}{2} \lVert Ax-y\rVert_2^2 + \lambda \lVert x\rVert_1\...
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1answer
444 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 ...
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1answer
78 views

Signal processing research idea [closed]

I am a graduate student in applied math, specializing mostly in harmonic analysis. My undergraduate studies were mostly in pure math but I realized I prefer the applied/computational side. I was ...
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1answer
444 views

How Can I Use MATLAB to Solve a Total Variation Denoising Problem?

The Total Variation Denoising Problem is given by: $$ \arg \min_{x} \frac{1}{2} {\left\| A x - y \right\|}_{2}^{2} + \lambda \operatorname{TV} \left( x \right) $$ Where $ $ is the Total Variation ...
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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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1answer
660 views

Adaptive filtering: Optimum filter length and delay

I'm trying to find the optimum filter length for an Adaptive Filtering, using RLS Algorithm. I'm using this design: So the "error" signal is the signal without noise (and that's the signal that I ...
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1answer
159 views

optimization of filter coefficients to given wordlength

It seems to me that this is a difficult mathematical problem where research is still carried on: Is there an efficient way to find fixed-point coefficients whose zeros are closest to those calculated ...
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0answers
382 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 ...
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1answer
666 views

Two-View 3D reconstruction using the sparse Levenberg–Marquardt algorithm

I have trouble implementing the Levenberg-Marguardt algorithm as described in the book Multi View Geometry in Computer Vision. To be more specific I have trouble calculating the partial derivatives ...
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1answer
604 views

How does parallel structure implementation of IIR speed up the process ? What happens in case of FIR?

I was learning about digital filter structures and there I came to know that parallel implementation of IIR filters speeds up the process and I understand that.But what I am not convinced of is that ...
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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 $y\in \mathbb{R}^m$ ...