Questions tagged [optimization]

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Estimate instantaneous frequency using LMS algorithm - optimization

I hope someone can help me with the following problem: I want to estimate the frequency of a soundfile that is composed of a sinusoid with varying frequency and additive white noise: $x[n] = sin(\...
2
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1answer
237 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
56 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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2answers
254 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 ...
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0answers
11 views

Optimizing a heating/cooling system for a particular input

Lets say I have a house with 2 rooms. One of them has a window that opens and closes T periodically. So the heat influx behavior of the window is like a square wave. There is an air conditioning unit ...
2
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1answer
129 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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3answers
88 views

How to Apply Statistical Algorithms of Signal Processing to Regulate Variation of a Curve?

Below I am posting 2 graphs. I want to regulate the curvature of first graph using some statistical methods such as use of standard deviations, and modulate my graph to look like second one. I am not ...
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1answer
2k 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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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
40 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
78 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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2answers
93 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 $$ {\...
3
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1answer
132 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 Richard G. Baraniuk - Compressive Sensing - Lecture Notes (Also on DocDroid), I came to know that minimum $ {L}_{1} $...
4
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1answer
619 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 $ \operatorname{TV} \left( \...
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1answer
89 views

Difference Between Iteratively Reweighted Least Squares (IRLS) and Sequential Quadratic Programming?

Part of my work is concerned with applications in Sparse Bayesian Learning and therefore I occasionally stumble over interesting papers in the field of compressed sensing. I recently read ...
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0answers
74 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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0answers
24 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
25 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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2answers
102 views

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

How would one implement the lock Orthogonal Matching Pursuit (BOMP) Algorithm?
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2answers
324 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}^{\ast} = \arg \min_{x} \left\{ \frac{1}{2} {\left\| A x - y \right\|}_{2}^{2} + \lambda ...
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1answer
44 views
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1answer
43 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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2answers
90 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 ...
2
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1answer
206 views

Optimization of Filter Coefficients to Given Word Length

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 ...
2
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1answer
79 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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2answers
125 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 ...
2
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1answer
97 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
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1answer
724 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 utilities a Wiener-like approach, ie it converges to the optimal (wiener) solution. I ...
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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 ...
1
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1answer
29 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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3answers
5k views

Librosa stft + istft - Understanding my output (which always seems too perfect) at varying window lengths

I've just started to use Python with Librosa for a DSP project I'll be working on. First thing I've been trying to do is determine my preferred parameters for the FFT window size, and hop-distance. ...
0
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1answer
74 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
92 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
153 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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0answers
26 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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1answer
310 views

Ideal Geometric Arrangement of Microphone Array

I'm going to have to give a bit of context for this question to make sense. I am working on a project which includes audio source localisation in 3-D space through TDoA (Time Difference of Arrival - ...
0
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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 ...
2
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1answer
414 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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1answer
200 views

How to Smooth Gradient Estimates for Steepest Descent Optimization

In steepest descent methods of minimizing a function $f(x), x \in \mathbb{R}^d$, it's common to approximate the gradient by finite differences: $\qquad\qquad \nabla f(x) \approx gradest( x; h ) \...
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0answers
57 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 ...
1
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2answers
84 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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2answers
69 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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1answer
122 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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5answers
20k views

Compressive Sensing Through MATLAB Codes

I am new to the topic of compressed sensing. I read a few papers about it by R.Baranuik, Y.Eldar, Terence Tao etc. All these papers basically provide the mathematical details behind it, i.e., Sparsity,...
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0answers
129 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
21 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
83 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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3answers
2k 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 $x$, ...
3
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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 ...
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1answer
64 views

Regularized Least Squares by Laplacian Operator - Optimal Value of the Regularization Factor (Lagrangian Multiplier)

Consider the cost function $$f(X,\lambda) = \|AX-b\|_2^2 + \alpha \|LX\|_2^2$$ $A:$Measurement matrix($R_{m\times n}$,$m \ll n$), $b:$observation vector($R_m$), $L:$Laplacian operator($R_{n \times n}...