Questions tagged [matrix]

is a mathematical object to be recorded in a [usually] rectangular array of elements of ring or field, which (table) is a set of rows and columns are located at the intersection of its elements. The number of rows and columns specify the size of the matrix.

28 questions with no upvoted or accepted answers
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67 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 ...
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161 views

Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori

I am implementing a Kalman filter (for a linear ODE system for now). My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
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183 views

Distribution of a signal covariance matrix

A common estimation problem in signal processing assumes the following signal model \begin{equation} \mathbf{r} = \sum_{i=1}^{Q}\alpha_i\mathbf{s}\left(w_i\right)+\mathbf{n} \end{equation} where $\...
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169 views

Can Cholesky outer product version result in negative square roots?

Say A is symmetric positive definite matrix , which means one necessary condition is diagonal entries of A are positive. If I do cholesky factorisation using outer product form, Can there be any ...
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18 views

A good reference for matrix completion

Does anyone know a complete reference or book on matrix completion?
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27 views

Estimating a matrix from another matrix

The problem is the non- negative matrix factorization of a matrix. Let me explain my problem I have an original matrix $A=\begin{bmatrix} 0.248437 &0.25198098 & 0.25396825 & 0.25077881\\ 0....
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67 views

1D as a 2D FFT - am I understand it properly

in one of my question about non $ 2^L $ points FFT I got answer with advice to read about that in following book: Rabiner, Lawrence R., and Bernard Gold. "Theory and application of digital signal ...
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49 views

Normalized LMS with a posteriori Error and Woodburry's Matrix Inversion

I was going through this paper and the author mentioned that we can prove the following using the Matrix Inversion Lemma (AKA Woodburry's Matrix Inversion Identity): Using matrix inversion lemma we ...
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150 views

What is the best way to determine the process noise matrix $\mathbf Q$ of a Kalman filter?

It seems like most of the resources online suggest to determine the values of the process noise matrix $\mathbf Q$ through trial and error. However sometimes trial and error doesn't work, so I would ...
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0answers
72 views

Help Understanding Radial Gaussian Filter

I am currently reading through Mueller's "Fundamentals of Music Processing" and I am trying to understand audio segmentation through the use of self-similarity matrices. Currently, my matrix looks ...
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26 views

Emulate signal loss of a pixellated detector in Python?

I have a matrix 64x64 where each cell represents the pixel of a pixellated detector. The spacial response of this detector decreases by going further from its center (that is, coordinates "31,31" or "...
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94 views

Sensor Data Fusion with Orientation Sensors in 3D Euclidian Space

Preconditions For measuring the position of a mobile device in 3D space, I utilize two sensors with different characteristics that measure device orientation. Sensor A (a combined sensor of ...
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39 views

Matrix expansion into bases

I have an image (that is a matrix), let's say of dimensions NxN. I then want to expand this matrix into M basis matrices (for the moment I'm still unsure how many M of these basis matrices I should ...
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106 views

How to replace Hadamard Product and Column wise addition with new Matrix operation?

Let $$ A= \begin{bmatrix} a_{1,1} & a_{1,2} & a_{1,3}\\ a_{2,1} & a_{2,2} & a_{2,3}\\ a_{3,1} & a_{3,2} & a_{3,3}\\ \end{bmatrix} $$ and $$ B= \begin{...
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61 views

Solving an Array Signal Processing Estimation Problem based on the Rayleigh Quotient

The Rayleigh quotient for a covariance matrix $\mathbf{C}$ and a non-zero steering vector $\mathbf{a}$ is given by $$ R(\mathbf{C},\mathbf{a}) := \frac{\mathbf{a}^H\mathbf{C}\mathbf{a}}{\mathbf{a}^H\...
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372 views

How to understand energy function in thin plate splines?

guys! I have carried out some experiments using matlab warp tools from here. But the results are not good, so I decide to read its original paper Principal Warps: Thin-Plate Splines and the ...
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1answer
13 views

What is the difference between positive matrix coefficients and negative matrix coefficients of an audio?

I have turned an audio file into an one dimensional array by using audioread function in matlab and found several positive and negative fractional coefficient values.What is the basic difference of ...
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1answer
14 views

Similarity or Relation between Walsh Hadamard Transform and Slant Transform

Is there any relation between Walsh Hadamard Transform and Slant Transform? Or is there any common property or similarity?
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39 views

Matlab: How to implement expectation of product of hermitian matrix

I want to implement the following equation in Matlab: $\mathbf {R}_\mathbf {z}^a(\tilde{f}) = \mathbb {E} \left[\mathbf {z}(\tilde{f}) \mathbf {z}^H(\tilde{f}+a) \right]$, $ \tilde{f} \in \left[0, ...
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18 views

Join 2 NMF models where dictionaries has hierarchical structure

I have two NMF models $A = W_1A_{dict}$ and $B = W_2B_{dict}$ (where the $W$ represents weight coefficient matrix). What is a good way to join two NMFs if I know each column of $B_{dict}$ is summed up ...
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2k views

How to calculate the scale, rotation angle and translation between 2 images if we know the homography result matrix?result

I got the result of findHomorgraphy in OpenCv. As below: Homography transform matrix: [-1.1534205416542787 0.7834287271121142 527.9064589440736 -0.2415444621693116 0.16412191792642924 ...
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397 views

Generating Wavelet family matrixes

We have unnormalized Haar matrix which, is for example, H4=[1 1 1 1;1 1 -1 -1;1 -1 0 0;0 0 1 -1] After normalizing it, we use for haar transform. I know how to ...
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27 views

Are there condition numbers associated with the STFT, DWT?

Recently I learned that the DFT has good numerical stability since it can be represented as an orthogonal matrix, which has a condition number of 1. Is it possible to represent the STFT and DWT as ...
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128 views

Matching 2 undirected weighted graph in matlab

Consider 2 undirected weighted graph as shown in figure.Consider first graph as G1 and second graph as G2.Graph G1 consist of vertices V={F1,F2,F3,F4,F5} and Graph G2 consist of vertices V={N1,N2,N3,...
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588 views

How to Prevent overflow/saturation in fixed point implementation of Fast Data Projection Algorithm

I am trying to implement an algorithm in real-time on a Fixed point DSP (The Blackfin from Analog Devices). The algorithm does a lot of stuff, but in the middle it performs an algorithm called "Fast ...
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560 views

3 Band Wavelet Transform In MATLAB

I am currently working on an audio watermarking project in MATLAB. I currently have a code I am using to construct a nxn 3 Band Wavelet Transform matrix. However, when I try to construct a matrix that ...
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1answer
305 views

Incoherence: Compressed Sensing (CS) vs Matrix Completion (MC)

I am seeking a clarification of the concept of Incoherence within the MC framework. Specifically, 1) the literature mentions the application of a "strong incoherence" given a set of assumptions. ...
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2answers
84 views

Image processing - Why is sum of values of a blurring filter = 1?

Usually, blurring filters have the sum of all the values in the filter matrix equal to $1$. Why is it so?