2
votes
0answers
18 views

Transforms with $O(N \log N)$ Complexity

Beside the Discrete Fourier and Walsh-Hadamard operators, are there any non-trivial, bijective operators that admit an evaluation algorithm of $O(N \log N)$ time complexity or better, whose inverses ...
1
vote
1answer
94 views

calculating an incoherence property

With respect to Matrix Completion and Compressive Sampling (CS) I'm trying to understand how to calculate an incoherence property μ between two bases Φ and Ψ. Getting this incoherence is important ...
1
vote
2answers
23 views

Data preprocessing

How would you preprocess 2 dimensional data to have 0 mean? Say you have a matrix $M $ that is $p \times q $. Would you calculate the mean of each row, get a vector of length $q $ and subtract each ...
0
votes
1answer
71 views

Bounds on least squares and weighted least squares estimator

I was wondering if I can get some help in getting bounds on the parameters estimated by least squares (LS) and weighted least squares (WLS) methods. Suppose our observation model is: $\mathbf{y} = ...
1
vote
0answers
49 views

Why process noise model is$ \dfrac{T^4}{4}$ in Kalman filter.

I am using Kalman filter for filtering noise on 2D object movement. I read a lot of examples, but no one has been explained, why noise model is distance powered by 2: $$ s \times s = \dfrac{T^2}{2} ...
1
vote
1answer
28 views

How to show quantisation error for frequency coefficient

I have the following question from an exam which reads: For the second question my answer is: 24 5 2 3 9 2 1 3 2 3 2 2 1 1 1 0 I am unsure of what formula ...
0
votes
1answer
83 views

(geometric) intuition of whitening

I found this http://cis.legacy.ics.tkk.fi/aapo/papers/IJCNN99_tutorialweb/node26.html But I still don't have an intuition of whitening. A diagonal covariance matrix means uncorrelated distributions, ...
5
votes
2answers
5k views

How do I - exactly - project a vector, onto a subspace?…

I am trying to understand how - exactly - I go about projecting a vector onto a subspace. Now, I know enough about linear algebra to know about projections, dot products, spans, etc etc, so I am not ...
1
vote
0answers
292 views

Fast Walsh–Hadamard transform generalization for non-power-of-two orders?

I have to process vectors through a Hadamard matrix of order N. If N is a power of 2, I can use the Fast Walsh–Hadamard transform; but if N is not a power of two (for instance, N=12), it is not ...
2
votes
0answers
149 views

Singular Value Decomposition

I want to decompose an image $A$ using the Discrete Wavelet Transform and then find the singular values, $S$, such that $A=USV$. I will then do the same to another image such that $B=USV$. I will ...