Questions tagged [optimization]

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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 ...
3
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1answer
487 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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0answers
59 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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2answers
86 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
81 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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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,...
3
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0answers
132 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
22 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
97 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
3k 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 $x$, ...
4
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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 ...
2
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1answer
79 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}...
5
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1answer
340 views

Approximating $ {L}_{0} $ Norm Minimization with Non Linear Convex Inequality Constraints using Reweighted $ {L}_{1} $ Minimization

I have an optimization problem consisting of the $ {\ell}_{0} $ norm as the objective and a nonlinear (convex) constraint as well as a linear constraint. I am wondering if the reweighted $ {\ell}_{1} $...
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2answers
661 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 ...
7
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1answer
397 views

Weighted Nuclear Norm Minimization for Image Denoising

Recently, I saw new published papers like Shuhang Gu, Lei Zhang, Wangmeng Zuo, Xiangchu Feng, Weighted Nuclear Norm Minimization with Application to Image Demonising [pdf]. about denoising images ...
2
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1answer
85 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 ...
17
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1answer
1k views

What Does Make an Error Surface Convex? Is It Determined by the Covarinace Matrix or the Hessian?

I am currently learning about least-squares (and other) estimations for regression, and from what I am also reading in some adaptive algorithm literatures, often times the phrase "... and since the ...
7
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1answer
138 views

Ideas on Matrix Factorization / Transformations for $ {L}_{1} $ Minimization

I am starting with a typical $\ell_1$ basis pursuit problem: $$ \min_{\mathbf{x}} \Vert \mathbf{x} \Vert_1 \quad \mathrm{s.t.} \quad \Vert \mathbf{ERx} - \mathbf{y} \Vert_2 \leq \epsilon, $$ where $\...
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1answer
80 views

Iterative Blind Sinus Signal Suppression

There are two real signals in the form of $A_i sin(wt+p_i), i=1,2$. Suppose frequency $w$ of both the signals is the same and amplitude $A_i$ and phase $p_i$ are different. The first signal has ...
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1answer
3k views

$ {L}_{0} $ Pseudo Norm Minimization in Compressive Sensing

I have recently taken up studying compressive sensing related papers. Some things are not very clear to me or may be I am not able to visualize the scenario as is said. Like how $l_0$ norm ...
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2answers
419 views

Significance of $ \lambda $ in Basis Pursuit

In basis Pursuit, L1 minimization is done to perform compressed sensing. In the literature there is a $ \lambda $ parameter used as a regularizer. What is its significance?
2
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1answer
127 views

Adaptive Filter Gradient Descent

The quadratic performance surface of an adaptive filter is a paraboloid. Its minimum can be found wherever the gradient is zero. However, since there are two types of paraboloids (elliptical and ...
1
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1answer
81 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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2answers
811 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 $\...
11
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0answers
668 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 ...
3
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0answers
76 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 ...
24
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5answers
16k views

What Is the Best First Order IIR (AR Filter) Approximation to a Moving Average Filter (FIR Filter)?

Assume the following first order IIR Filter: $$ y[n] = \alpha x[n] + (1 - \alpha) y[n - 1] $$ How can I choose the parameter $ \alpha $ s.t. the IIR approximates as good as possible the FIR which is ...
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0answers
44 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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1answer
126 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 ...
2
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1answer
5k views

Determine the optimum receiver and the corresponding $P_{eM}$ for an AWGN channel

I have a source that emits $M$ equiprobable messages, which are assigned signals $s_1, \dots,s_M,$ that are equidistant by $a$. That is, if we plot the $s_k$ signals in a horizontal axis they are dots ...
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2answers
458 views

Convex Optimization in Signal and Image Processing

In signal processing, convex optimization plays a useful role in problems such as sparse signal recovery and filter design. What other places does convex optimization appear? For example, in ...
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0answers
153 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
78 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
87 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. ...
2
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2answers
702 views

Lagrange Multipliers Optimization - Complex Functions

I want to optimize a sum of complex frequency responses (complex sum is SPL, sound pressure level as a complex function of distance) of a number of loudspeakers, say 10. There is a reference, desired ...
1
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0answers
171 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 ...
2
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1answer
1k views

Multiple parallel IIR bandpass filters with different centre frequencies combined into one filter for optimisation… possible?

Before I begin, I have read these already: IIR filter parallelization Concept of combining multiple FIR Filters into 1 FIR filter I am processing audio using Csound in a high performance real time ...
0
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1answer
97 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 ...
0
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1answer
92 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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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 ...
7
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1answer
1k 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 ...
1
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0answers
448 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 ...
0
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1answer
759 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 ...
3
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1answer
772 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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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 $y\in \mathbb{R}^m$ ...
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2answers
264 views

How to improve filter quality at low fs

This my 1st post here. I'm using this impulse invariant (MZT) based method to calculate coefficients for biquad digital filter (for RIAA and non-RIAA de-emph.): ...
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0answers
352 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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0answers
108 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 ...
2
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1answer
2k views

Fitting an IIR filter to a complex transfer function

anybody knows of better ways to fit an IIR filter to a complex transfer function than Matlab's invfreqz.m? I'm implementing a little transfer function fitting ...
2
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1answer
350 views

Optimized 2D wavelet transform using FFT

I'm currenty aiming to optimize my fast wavelet transform (FWT) algorithm for 2D signals (images). It works as follows: one iteration of 1D FWT does convolution of 1D input data with a selected 1D ...