# Questions tagged [optimization]

The tag has no usage guidance.

118 questions
Filter by
Sorted by
Tagged with
25 views

22 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 $f^{t}x$ ...
47 views

### Solving LASSO (Basis Pursuit Denoising Form) with LARS

I'm now working on using LARS (Least Angle Regression) algorithm to solve a LASSO problem in Basis Pursuit Denoising form like: \begin{align*} \quad && \arg \min_{\beta}{\left\| y - X\beta \...
106 views

### On the Measurement Matrix Used for Compressing Sensing

Assume we have a matrix $x$ of size $(8,8)$ where each column is considered to be sparse with degree of sparsity equals to $4$. it means that every column can have $4$ zeros and $4$ non-zeros values ...
50 views

### On the Use of OMP Algorithm to Estimate Sparse Vector

As known, Orthogonal Matching Pursuit (OMP) Algorithm is to recover the sparse channel after convolution with another vector. But when I implement that in MATLAB, I don't get the sparse vector ...
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 ...
52 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 ...
126 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 ...
26 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 ...
28 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 ...
60 views

### Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm - Fix Given Code [closed]

This is my implementation which doesn't work: ...
178 views

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

How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
88 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 ...
54 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 ...
103 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. ...
35 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 ...
Recently, I am reading paper . 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 $$\mathbf{r} = \... 1answer 77 views ### Efficient correlation of a low duty cycle training sequence Is there a way to efficiently correlate a training sequence that is N samples long, framed at M samples where M >> N, with L occurrences of such frames (see below). For the pedants, the training ... 0answers 30 views ### Bundle adjustment optimization parameters While reading the Wikipedia article on Bundle adjustment, I came across the following objective function used to represent the bundle adjustment problem. I have two questions regarding this objective ... 2answers 166 views ### Constrained LASSO Problem -  {L}_{1}  Regularized Least Squares with Linear Equality Constraints I have an optimization question. I want to solve the following problem:$$ \arg\min_S\frac{1}{2}\|s-c\|_2^2 +\lambda\|\Phi s\|_1 \mbox{ s.t. } As = 0 $$in which \Phi is the wavelet transform ... 0answers 60 views ### Optimal sensor placement for 3D TDoA positioning Suppose there is a rectangle indoor area, we want to locate different positions within this area using TDoA estimations. 5 sensors are placed to obtain optimal 3D positions with TDoA errors, we only ... 1answer 73 views ### Promote the Orthogonality between Rows of  S  I have a question. Suppose we want to solve an optimization problem: Consider S \in \mathbb{R}^{N \times T}, T >> S$$\min_{S} f(S) \mbox{ s.t. } SS^T \mbox{is diagonal}$$Which means each ... 2answers 86 views ### How do you properly organize data to compute multiple (independent) recursive filters at the same time taking advantage of SIMD instructions? I'm processing multiple (independent) Exponential Moving Average 1-Pole filters on different parameters I have within my Audio application, with the intent of smooth each param value at audio rate: <... 2answers 88 views ### How to efficiently control an FIR's magnitude response by altering its phase spectrum Question: Extensively searching the space of all possible vectors of length n to satisfy a (non-overdetermined) requirement is possible in principle. Hence, there is a way to calculate a complex ... 1answer 52 views ### Wireless Body Area Networks with Minimum Energy Consumption [closed] For adaptive compressive sensing(cs),the sensing matrix is related to the input signal. For example, in rakeness-based(cs), the sensing matrix is obtained by solving an optimization problem which ... 2answers 57 views ### Control optimization problem I am running into a problem where I have a control system S[t] that takes a control C[t], so that$$S[t+1] = H(C[t,t-1,...], S[t,t-1,...])$$the response of the system is the history of controls ... 0answers 135 views ### How to implement the RLS for matrices I need to implement the RLS algorithm but it's for matrices instead for vectors, I have made the below code, but still something wrong is not working well, EDIT: The code should be done as below, ... 0answers 23 views ### Improve NMF for data with partial overlaps in multiple groups? I want to use NMF to separate true sources from data. My data is in group structure with overlap elements. For example (in the smaller version) group1: contains A,B,C,D,E,F,G patterns group2: ... 1answer 109 views ### How Is Mixed Norm ( {L}_{1, 2 }) Better than  {L}_{1}  Norm for Sparse Representation? Using  {l}_{1} -norm regularization for the purpose of achieving sparsity of the solution has been successfully applied a lot. But many times, I found the paper using mixed-norm instead of l_1-... 1answer 203 views ### How to Formulate a Constraint Which Ensures All Variables Have the Same Sign I'm trying to include a constraint in my problem (to be solved by any convex optimization solver). Let {a,b,c,d ...} be a finite set of continuous variables. How to formulate a constraint which ensure ... 0answers 69 views ### Designing a fast linear operator with \pm 1 entries with low condition number and low Hamming distance between consecutive rows I need to design a matrix for compressive imaging where each row represents an N-pixel filter in a focal plane through which light is masked, summed, and measured (think of Rice's single-pixel ... 3answers 4k views ### Derivative with respect to complex conjugate I have a real function C of a complex vector x. While taking the gradient of the function C for minimising the same, why do we take the derivatives with respect to the complex conjugate of x, ... 1answer 146 views ### Sequential Non Linear Least Squares Problem I have the the following non-linear function,$$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)$$with unknown (but deterministic) parameters A_k,\mu_k,\... 1answer 90 views ### Sparse Recovery Best Algorithms In the big data era, in order to control the cost, complexity, and bandwidth of collecting and processing high-dimensional data systems, it is critical to exploit models that ... 2answers 3k views ### Fastest Available Algorithm to Blur an Image (Low Pass Filter) Iam working with a camera that produces ugly artifacts: by using ANY blur filter on the camera's output the visual quality improves drastically: The above image was created using OpenCV's cv::... 1answer 98 views ### The Gradient Operator of a Vectorized Image in Matrix Form I have this optimization problem:$$ \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) - \...
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 ...