1
vote
0answers
43 views

How does SVD work?

Trying to find information, and, no-one seems to know the answers. I have a time-series, represented by $T = [0, 1, 1, 0, \ldots, n]$ the time series is then transformed into the Spectral results: ...
2
votes
0answers
37 views

Error bounds in representing a vector using a truncated Moore-Penrose biorthogonal basis

I was reading and trying to reproduce the results in the arXiv preprint of Periodic Gabor Functions with Biorthogonal Exchange: A Highly Accurate and Efficient Method for Signal Compression by Asaf ...
1
vote
1answer
157 views

Can the measurement matrix used for compressive sensing be a sparse matrix?

I am interested in analyzing Compressive Mechanism: Utilizing Sparse Representation in Differential Privacy. In my research, the measurement matrix $A\mathbb \in R^{m \times n}$ needs to be sparse. ...
3
votes
2answers
998 views

Waves of differing frequency are orthogonal - help me understand

I know that sinusoidal waves of different frequencies are orthogonal to each other. For instance: ...
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
1answer
61 views

Find the transform

I have the paper with 3 points on it. I have also a photo of this paper. How can I determine where is the paper on the photo, if I know just the positions of these points? And are 3 points enough? It ...
6
votes
2answers
234 views

Usage of inverse Laplace transform

At my current study level in college, use of inverse Laplace transform is not mentioned well - textbooks say "use tables." So, can anyone show me how to use inverse Lapalce transform? And also proof? ...
1
vote
1answer
121 views

What does it mean to convolve a matrix with a kernel?

I have a Matrix, M, of dimensions width x height. The problem is to apply the [-1, 0, 1] filter along the x and y axis (i.e. convolve the image with [-1, 0, 1] kernel along horizontal and vertical ...
1
vote
1answer
178 views

Should mean be subtracted before convolution?

Suppose I have a signal in the form of N real numbers. I am searching for a continuous pattern within this signal. The pattern is represented by M real numbers. (M < N) To find the pattern's ...
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 ...
2
votes
2answers
387 views

normalization of a linear combination

I'm a newbie at this forum, so I hope, that this question is not so silly. Let's have some filter $F$, which is a linear combination, thus $F = \sum_{i=0}^{i=N}\alpha_ib_i$, where $\alpha_i$ are ...
12
votes
3answers
423 views

Fast computation/estimation of the nuclear norm of a matrix

The nuclear norm of a matrix is defined as the sum of its singular values, as given by the Singular Value Decomposition of the matrix itself. It is of central importance in Signal Processing and ...