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2
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0answers
40 views

When does l1 regularisation give a sparse solution?

I was maximising a likelihood function, which is convex. I know that the system has a K-sparse solution. I wanted to know the conditions (or some sufficient conditions) on the likelihood function ...
0
votes
0answers
69 views

L0 norm minimization in compressive sensing

I have recently taken up studying compressive sensing related papers. Some things are not very clear to me or may be i am not able to visualize the scenario as is said. Like how L0 norm minimization ...
0
votes
1answer
50 views

Iterative blind sinus signal suppression

There are two real signals in the form of $A_i sin(wt+p_i), i=1,2$. Suppose frequency $w$ of both the signals is the same and amplitude $A_i$ and phase $p_i$ are different. The first signal has ...
0
votes
0answers
15 views

How to smooth gradient estimates for steepest descent optimization

In steepest descent methods of minimizing a function $f(x), x \in \mathbb{R}^d$, it's common to approximate the gradient by finite differences: $\qquad\qquad \nabla f(x) \approx gradest( x; h ) ...
1
vote
1answer
62 views

L2-optimal IIR Filters

It is widely known that matching a FIR filter of fixed length to a band model is an unconstrained QP-problem. The matlab function "firls" implements a solution to this problem. Basically, one ...
0
votes
0answers
13 views

Finding lowest gradient path through multiple sets of samples

I have a noisy 2d signal I have sampled at multiple orientations, let's say 4 . I know that the orientation will either catch the signal accurately, or be much too high or too low. If the true ...
1
vote
0answers
74 views

Optimal filter bank from SVD/PCA

Given a million data points in say 100d, is there a way to generate an optimal filter bank of say 20 filters from an SVD of the data ? Call the 100d space $F$ (as in Frequency), with coordinates ...
1
vote
0answers
67 views

Any idea how can I optimize morlet wavelet parameters by Heisenberg uncertainty principal and Shannon entropy?

Based on a paper in here, they have proposed a method to optimize morlet function parameter. I have tried to implement their technique, but I can't get rational results. any idea? In here you can see ...
0
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0answers
124 views

Digital Image Processing - Contemporary Research Topics

I need to propose a masters degree topic, and I'd like it to be in digital image processing. What are currently relevant topics in this area? I suppose that I'm looking for some kind of ...
3
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0answers
50 views

Ideas on matrix factorizations and/or transformations for $\ell_1$ minimization

I am starting with a typical $\ell_1$ basis pursuit problem: $$ \min_{\mathbf{x}} \Vert \mathbf{x} \Vert_1 \quad \mathrm{s.t.} \quad \Vert \mathbf{ERx} - \mathbf{y} \Vert_2 \leq \epsilon, $$ where ...
2
votes
1answer
106 views

Ideal geometric arrangement of microphone array

I'm going to have to give a bit of context for this question to make sense. I am working on a project which includes audio source localisation in 3-D space through TDoA (Time Difference of Arrival - ...
4
votes
0answers
208 views

fit theoretical spectrum to simulated one

I have a bunch of simulated time series, for which I can compute the power spectrum. Generally, the simulated power spectrum can be sketched as follows: I now aim to calculate the features of the ...
1
vote
1answer
491 views

Determine the optimum receiver and the corresponding $P_{eM}$ for an AWGN channel

I have a source that emits $M$ equiprobable messages, which are assigned signals $s_1, \dots,s_M,$ that are equidistant by $a$. That is, if we plot the $s_k$ signals in a horizontal axis they are dots ...
2
votes
1answer
101 views

How to calculate signal which is not changed by a filter?

Suppose that there is a FIR filter F and a signal S. The filtered signal is the convolution of F and S, F * S. The problem: how to calculate a signal S' such that F * S' = S' (the filtered version ...
2
votes
0answers
60 views

Phong Reflection Model Parameters

Question: Can anyone refer me the Phong reflection model parameters for a face image taken for web-cam? Details: I am doing 3D reconstruction of 2D images using 3D Morphable Model as in this paper ...
4
votes
1answer
110 views

Finding length of period in time domain data

I have a series of measurements of a signal source, which emits a periodic signal at an unknown interval time of p seconds. Detecting the signal is not easy so I am ...
13
votes
1answer
355 views

How to tell if an error surface is convex? (Is it determined by the Covarinace matrix or the Hessian)?

I am currently learning about least-squares (and other) estimations for regression, and from what I am also reading in some adaptive algorithm literatures, often times the phrase "... and since the ...