# Tag Info

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Accepted

### Sequential Form of the Least Squares Estimator for Linear Least Squares Model

There are really great answers. I will try to give the Sequential Least Squares approach which generalizes to any Linear Model. Sequential Least Squares Model We're after solving the Linear Least ...
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### The Gradient / Derivative of Least Squares of 2D Image Convolution

The easiest approach would be writing each case using Matrix Form of the convolution. In this answer we assume the discrete convolution is applied only on valid support (Matching MATLAB's ...
Accepted

Accepted

### Weighted Nuclear Norm Minimization for Image Denoising

Most of the Denoisers in Image Processing make a simple assumption - The data has small number of freedom degrees while noise has high number. Hence if we try to represent the given noisy data with ...

### Proof of complex conjugate symmetry property of DFT

Remember that $e^z$ has a very different meaning than $e^x$ (taking $z\in\mathbb{C}$ and $x\in\mathbb{R}$). If the exponent was real, then, as you state in your question: $$e^x = 1 \iff x=0$$ ...

### Proof of complex conjugate symmetry property of DFT

Did you ever wonder about where $\pi$ came from? Watch out... Let us first draw this weird function complex exponential $e^{-2j\pi t}$ for several discrete values of $t\in[0,10]$ (the little blue ...

### The Least Norm Solution of Under Determined Linear System

Least Squares solution is always well defined for Linear System of Equations. In your case, which is under determined it means there are many solutions to the Linear Equations. The Least Squares ...
Accepted

### How Can PCA Be Used in Image Analysis

Imagine you have a set of 10,000 images (32 x 32) of faces. An intuitive way is to think they have a lot in common. One step farther would be that if you take one of the faces you could generate it ...
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### Minimize the Cost Function of Values of Vectors Based on Their Amplitude

Since there is no prior at the Vector level this is basically element wise problem. Moreover, if we assume the noise to be White Noise with zero mean then the answer can be very simple. Since the ...