Hot answers tagged

11 votes
Accepted

Accessing Maximum Value from a Singular Value Decomposed Matrix

The SVD Decompose the image into the (One way to look at it) many matrices. For instance, given an Image $ I $ its SVD is given by: $$ I = U S {V}^{T} = \sum_{i=1}^{\textrm{rank}(I)} {s}_{i} {u}_{i} {...
user avatar
  • 40.4k
10 votes
Accepted

How to Check Separability of 2D Filter / Signal / Matrix

Nilesh Padhi, Welcome to the DSP Community. The classic definition of separable means the data (2D) given by $ X \in \mathbb{R}^{m \times n} $ can be written as: $$ X = \sigma u {v}^{T} $$ Where $ \...
user avatar
  • 40.4k
9 votes
Accepted

How to Decompose a Separable Filter?

Indeed you can do that. You may look on my answer to How to Prove a 2D Filter Is Separable? By the SVD for any filter $ A $: $$ A = \sum_{i = 1}^{n} {\sigma}_{i} {u}_{i} {v}_{i}^{T} $$ Since we'...
user avatar
  • 40.4k
7 votes
Accepted

Questions on the Generalized Tikhonov Regularization

One way to interpret the Tikhonov Regularization is using the Maximum A Posteriori (MAP) framework. Lets' say we have a model of the form: $$ \boldsymbol{y} = H \boldsymbol{x} + \boldsymbol{n} $$ ...
user avatar
  • 40.4k
6 votes
Accepted

Regularization for Inverse Problems using the Singular Value Decomposition (SVD)

Similar to The Concepts Behind SVD Based Image Processing the horizontal axis are the samples index of the SVD basis. The idea in the chapter you linked is generalizing the Wiener Filter. While the ...
user avatar
  • 40.4k
5 votes
Accepted

Variational Regularization Method in Image Processing

This is an example of the Fidelity Term and Prior Term model. In many Inverse Problems we assume some model on the additive noise. This part is modeled by the Fidelity Term ($ \mathcal{D} \left(A \...
user avatar
  • 40.4k
5 votes
Accepted

The Concepts Behind SVD Based Image Processing

You may think on the SVD as a generalization of the Discrete Fourier Transform. Namely, it is generates an orthogonal basis to represent the data. The nice thing about it, it generates the basis ...
user avatar
  • 40.4k
5 votes

Denoise Techniques When Clean Signal and Pure Noise Are Available

If the data is stationary and the noise is white then you should use the Wiener Filter. If data isn't stationary you should look into the family of adaptive filters (LMS Filter and RLS Filter for ...
user avatar
  • 40.4k
4 votes
Accepted

What are the advantages and disadvantages separability of Gaussian 2D filter?

Assuming the simplest case with a square image $x[n,m]$ of size $N \times N$ and a square filter kernel $h[n,m]$ of size $M \times M$, the raw 2D convolution to produce the, cropped, output image $y[n,...
user avatar
  • 26.7k
4 votes

Accessing Maximum Value from a Singular Value Decomposed Matrix

[EDIT: some code made available] A common framework for (multivariate) image processing is to suppose that its useful features (edges, textures, spectral correlation) contain redundancy, while the ...
user avatar
4 votes
Accepted

How Does Mean Centering Affect the Result of Using SVD to Compress Images?

I will try to illustrate why it is important to remove the Mean from data when doing the PCA (SVD is the tool to basically do the PCA approach to dimensionality reduction -> Compression). If the data ...
user avatar
  • 40.4k
4 votes
Accepted

SVD vs matched filter

That's not true, it's not better. The thing is: the matched filter just implements the projection in the signal vector space, onto the signal vector itself (or a multiple thereof). (You'll find ...
user avatar
3 votes

why use svd() to invert a matrix?

The two methods differ, above all, by their applicability to matrix classes. col (cholesky) decomposes Hermitian, positive-definite rectangular matrices into the ...
user avatar
  • 1,415
3 votes

Where is truncated-SVD image compression actually used?

A first difficulty with your question is that "usual instances" may not be fully publicized nor documented. A second one is related to the fact that "compression standard" are ...
user avatar
3 votes

Denoise Techniques When Clean Signal and Pure Noise Are Available

I'm not sure I understand the question, but if you have the exact waveform you want to recover, you can basically employ a matched filter to detect the existence of the signal in the acquired data. ...
user avatar
3 votes
Accepted

How to express one image in terms of another one

I found an answer which is good-enough for me. As @Stanley Pawlukiewicz has pointed out in the comments, this is hard to do for a general case when there is little correlation between the images. I, ...
user avatar
3 votes
Accepted

Could not construct original matrix using SVD

Don't have enough reputation to comment but you need to use the conjugate transpose in your formula for the result to be correct. So try stftb=U*S*V'; in the last ...
user avatar
3 votes

Image compression using SVD in MATLAB

The typical thing to do is the low-rank approximation on separate channels. Assume that $C$ is a channel of the RGB image $I$: ...
user avatar
  • 5,207
2 votes

Problem with Covariance matrix using diagonal loading involved in calculation of eigenvalues

You can write $$ R=YY^H $$ where $Y$ is a matrix of size $N\times N_f$ and $N$ is the dimension of $y_k$. $Y$ contains all the measured $y_k$ as its columns. Then, the rank of $R$ is upper bounded ...
user avatar
2 votes

Where is truncated-SVD image compression actually used?

It has been said that the DCT reasonably closely matches the KLT for a representative set of images. KLT is essentially the same as PCA, I believe and SVD is only a different way to compute the same? ...
user avatar
  • 2,186
2 votes
Accepted

Subspace decomposition

You can rewrite the equation in a block matrix form: \begin{eqnarray}X &=& U_s \Lambda_s V_s^H + U_n \Lambda_n V_n^H \\ &=& \left[ \begin{matrix} U_s & U_n\end{matrix} \right] \...
user avatar
  • 2,686
1 vote
Accepted

Hankel Matrix SVD Denoising

A simple approach is to just take the last value of your time series and keep repeating it. If I repeat the last value 100 times, then I still get the large drop at the end, but the repetition means ...
user avatar
  • 22.3k
1 vote

System Identification with a Limited Bandwidth Input Signal and Region of Interest

Can't you just use the pseudo-inverse? That'll mean instead of: $$ \hat{\mathbf{h}} = (\mathbf{X}^{T}\mathbf{X})^{-1} \mathbf{X}^T \mathbf{y} $$ you use $$ \hat{\mathbf{h}}_{\tt pseudo} = (\mathbf{...
user avatar
  • 22.3k
1 vote

System Identification with a Limited Bandwidth Input Signal and Region of Interest

The reason x[n] must be white is because the solution will effectively spectrally weight the channel response based on the amount of energy present in each spectral frequency location. A white noise ...
user avatar
  • 37.1k
1 vote

Denoise Techniques When Clean Signal and Pure Noise Are Available

If noise is available and it is sure that noise will remain same/almost same for entire duration then one can go for Spectral Subtraction or Wiener filter techniques for noise reduction, which will ...
user avatar
1 vote

How to extract features from nonstationary signal using SVD (singular value decomposition)?

What you're describing is a spectrum estimation based on signal representation in a vector space spanned by eigenvectors of a particular matrix generated from your signal observation. That reminds me ...
user avatar
1 vote
Accepted

MUSIC algorithm derivation

The piece I was missing was the distribution of the initial phase values $\varphi_1$ and $\varphi_2$. It is standard to assume that these are uniformly distributed [^]. This leads to: $$ \mathbf{R_x} =...
user avatar
  • 4,014

Only top scored, non community-wiki answers of a minimum length are eligible