Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [svd]

25 questions
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1 answer

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

Given: x(n1,n2) = {1 ,n1=0,n2=0 ; 2 ,n1=1,n2=0 ; 3 ,n1=0,n2=1 ; 6 ,n1=1,n2=1 } How could one prove it is separable?
Nilesh Padhi
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5
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1 answer

The Concepts Behind SVD Based Image Processing

I am interested in information about the output of SVD of the matrix. Mathematical part of SVD process is clear to me but I don't understand how to read figures with graphs of SVD of a matrix. As I understood vertical axis represents singular…
Novak Djokovic
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How to Decompose a Separable Filter?

I have done some research on the Internet and I have found that a given 2D mask is separable if it exists only a singular value of that matrix. For example, given the following matrix: $$A = \begin{pmatrix} 1 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 1…
Josemi
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5
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3 answers

Denoise Techniques When Clean Signal and Pure Noise Are Available

I have the clean version of the signal. I can obtain the environmental noise. I want to apply an effective denoising technique on a noisy signal (i.e., clean plus environmental noise). Some observations: The noise to signal ratio is extremely…
dr.doom
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2 answers

Accessing Maximum Value from a Singular Value Decomposed Matrix

I have read few image enhancement papers, where an image is enhanced in transformed domain using either DCT (discrete cosine transform) or DWT (discrete wavelet transform) with SVD (singular value decomposition). An example is given in Enhancement…
Mayank Tiwari
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4
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1 answer

Questions on the Generalized Tikhonov Regularization

My first question is about the quadratic functional that is used in generalized Tikhonov regularization: $$\Psi(f)=\frac{1}{2}\|f\|^2_\Gamma=f^T\Gamma f.$$ In the above equation what does $\Gamma$ represent, some special matrix? Then, I don't…
Novak Djokovic
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4
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1 answer

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

I am reading these lecture notes on Optimisation and Inverse Problems in Imaging, and I have difficulties understanding how figures on page 20 (Figure 3.2) or page 21 (Figure 3.3). Precisely, I don't understand what numbers on horizontal and…
Novak Djokovic
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4
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1 answer

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

I have been learning about using the Singular Value Decomposition to find low rank approximations to matrices. I had an image which I converted to a matrix. I regarded each row of the matrix as a 'data point'. I did two things: Found the mean of…
Noppawee Apichonpongpan
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4
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2 answers

MUSIC algorithm derivation

Setup Suppose we have a complex $L\times 1$ signal $\mathbf{x}$ with two tones at (unknown) frequencies and phases defined as: $$ x_n = A_1 e^{j \omega_1n + \varphi_1} + A_2 e^{j \omega_2n + \varphi_2} $$ for $0 \leq n \leq L-1$. We observe…
Atul Ingle
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1 answer

Variational Regularization Method in Image Processing

I would like to understand better variational regularisation methods in image processing. In particular, the formulas in this image: Why formula (3.13)? In the notes that I read I cannot find anything about its background, why is the solution of…
Novak Djokovic
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2
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1 answer

Hankel Matrix SVD Denoising

I have performed Hankel Matrix Singular Value Decomposition de-noising to smooth out my univariate time series. It is the close price of EUR/USD exchange rate. Here is a picture: The problem I have is that the end of the data seems erroneous. How…
DomIsAwesomee
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calculate or decompose a Fourier transform signal amplitudes with unknown weights on sources

migrated from math-se... I am trying to calculate , or approximate the solution of following Fourier-sine transform problem that can be expressed as a contributions of periodic sources $f_i(x)$ and weights $a_i(x)$ : $$F(k) = \int_{0}^\infty …
dpdp
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2 answers

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

Given a FIR filter $h[n]$. Its action can described as: $$ \mathbf{y} = \mathbf{H} \mathbf{x} \\ \mathbf{y} = \mathbf{X} \mathbf{h} $$ where $\mathbf{H}$ and $\mathbf{X}$ is a Toeplitz matrix. If $h$ is unknown, Least Squares with a white Gaussian…
divB
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Problem with Covariance matrix using diagonal loading involved in calculation of eigenvalues

I have the following problem : I'm calculating the sample covariance matrix in the frequency domain ( $y_{k}$ is the FFT of a time domain $k_{th}$ symbol vector signal , basically a simulated received signal) as…
Ricardo García
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Where is truncated-SVD image compression actually used?

What are some instances of real-world sensors, cameras, filetypes, or datasets whose image compression method is (at least mostly-based on) the truncated-SVD?
Zim
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