# Questions tagged [optimization]

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### Multi-objective Shortest Path Problem

I am attempting to solve a shortest-path algorithm with Dijkstra. However, I have multiple cost functions. I am eager to combine these costs. What is the best and most accepted way of doing this ...
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### How to update point spread function of blind deconbolution by conjugate gradient?

There is an unblurred image $g$ and a blurred image $x$. Their relationship is expressed by the following formula using $psf$(point spread fucntion, size is $5×5$ kernel). $g = x \otimes psf\tag 1$ ...
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### Why are different methods used to optimize energy function for optical flow and stereo vision?

Optical flow and stereo vision both try to estimate dense correspondence from each pixel in one image to matching pixel in another image. For optical flow, the two images are taken from the same ...
113 views

### How to Solve the Image Dehazing Problem Using ADMM?

I want to solve the image dehazing problem using ADMM. I want to use the proximal algorithm to optimize each element. I refer to this treatise: Efficient image dehazing with boundary constraint and ...
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### How to Solve Blind Image Deblurring with Total Variation (TV) Prior Using ADMM?

As a continuation of the question How to Solve Non Blind Image Deblurring with Total Variation Prior Using ADMM? I would like to understand how could one solve the Blind Deblurring (Deconvolution) ...
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### Optimization of square matrix multiplied with another matrix to have the final result a unitary matrix

I have a square matrix $D$ whose size is $m \times m$ multiplied with another $m \times m$ square matrix $C$, I need to optimize the matrix $C$ to have a unitary matrix $DC$. I mean optimize the ...
43 views

### How to Solve an Image Deblurring Problem by Variational Methods Using ADMM?

Following up on a previous question, I wanted to understand how to solve an image deblurring problem using Variational methods in matlab or julia. Given some original blurry image $f$, I would like to ...
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### How to Solve Non Blind Image Deblurring with Total Variation Prior Using ADMM?

How could one use the Total Variation frame work to solve the Deblurring problem? Specifically using the ADMM as a solver. One could assume the blurring operator is known, linear and shift invariant. ...
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### Is Sum of Absolute Value / ${L}_{1}$ Norm of Differences Convex?

I'm not sure how to approach this exercise. One idea is to derive it w.r.t z, show that there is a min-extremum at $z=f_k$ and then show that for each value from the right and the left of the loss ...
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### sampling using L1 optimization

As much as I understand the F should be the interval medians (correct me if I wrong), according to the next slide, where is also the Loss function defined: What I don't understand is the next note in ...
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### Transform a data set by exploting the vectorfield

I am somewhat new in the field of Digital Signal Processing / Image processing. As shown in the figure, I have 4 straight lines $f_i(x)$ with $i = 1,\dots, 4$ that pass through $g(x)$. Similiarly ...
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### Minimize the Cost Function of Values of Vectors Based on Their Amplitude

I have two vectors $X = [x_1,x_2,x_3,x_4]$; and $Y = [y_1,y_2,y_3,y_4]$; I know that $|x_1|$ = $|y_1|$, and $|x_2|$ = $|y_2|$,... so on. it means the difference is only in the sign. it might be ...
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### Optimization of harmonics calculation

I need to compute the sine and cosine of an argument along with n "harmonics" \begin{matrix} \sin(x) & \cos(x) \\ \sin(2x) & \cos(2x) \\ \cdots \\ \sin(nx) & \cos(nx) \end{...
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### Compute Hann window without cos function

In an environment with limited memory and computing power it is interesting to be able to generate a Hann window without using a cache or repetitive calling of expensive functions such as sine and ...
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### How to find the value of regularization parameter/s when having one or multiple priors

I am working on a image reconstruction framework, specifically interferometry. In simple words we have data that is pertubated by noise, say $$V^o_i = V_i + \sigma_i$$ Where $V^o$ is a complex ...
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### How can I infer the cost function from Kruppa's simplified equations

The following equations are Kruppa's simplified equations used in camera autocalibration. My objective here is to infer the cost function(Error Function) from this equations, So I can minimize the ...
112 views

### Quadratic Programming with Linear Equality Constraints

I need to solve an equality constrained minimization problem as give below $$\min_{\textbf{w}} \mathbf{w}^TR\mathbf{w}$$ such that $$X\mathbf{w} = \mathbf{1}$$ where $R\in \mathbb{R}^{n\times n}$ is ...
if $\mathbf x$ is $N\times 1$ sparse vector, and $\mathbf A$ is an $M\times N$ matrix with $M<<N$, and we measure $\mathbf y=\mathbf{Ax}$, then compressed sensing theory tells us that we can ...