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3
votes
1answer
57 views

Lagrange Multipliers Optimization - Complex Functions

I want to optimize a sum of complex frequency responses (complex sum is SPL, sound pressure level as a complex function of distance) of a number of loudspeakers, say 10. There is a reference, desired ...
1
vote
1answer
46 views

Multiple parallel IIR bandpass filters with different centre frequencies combined into one filter for optimisation… possible?

Before I begin, I have read these already: IIR filter parallelization Concept of combining multiple FIR Filters into 1 FIR filter I am processing audio using Csound in a high performance real time ...
0
votes
0answers
18 views

Quantization threshold selection

I have the 256-bin histogram representing a distribution of the values taken by a certain descriptor element. This descriptor element takes the values in 0-255 range, hence 256 bins. I want to ...
5
votes
0answers
118 views

Will an unscented Kalman filter be “as good” as other optimisation algorithms for this problem?

I want to calibrate a tri-axis magnetometer when a tri-axis gyroscope is also available. I am fairly certain I can solve this problem using various optimisation algorithms, but I would prefer to use ...
1
vote
1answer
65 views

Optimized 2D wavelet transform using FFT

I'm currenty aiming to optimize my fast wavelet transform (FWT) algorithm for 2D signals (images). It works as follows: one iteration of 1D FWT does convolution of 1D input data with a selected 1D ...
0
votes
1answer
30 views

Optimized resource allocation problem

I am from ECE background and trying to solve channel allocation problem. Let's assume I have three users and three available channels. I would like to allocate channel among them in such a way that ...
0
votes
0answers
9 views

Subgradient method for k-means like problem

I want to solve k-means-like problem. But at first, I wonder that we can apply subgradient method to k-means problem. We want to find the optimal clustering $S = (S_1,S_2,...,S_k)$ such that $$ ...
3
votes
0answers
78 views

Signal reconstruction in compressed sensing with a simple vector signal as an example

While going through the different types of reconstruction algorithm as mentioned in lecture notes in Compressed Sensing by Richard G. Baraniuk, I came to know that minimum $l_1$ norm reconstruction is ...
1
vote
1answer
44 views

find cross correlation lag by optimization

I have data from many closely located sensors (geophones). These are often contaminated with coherent noise which I need to remove. Some of the most effective de-noising methodologies work if the ...
1
vote
1answer
39 views

Filtering performance on Poisson noise with quadratic data-fidelity

We recently performed a work on signal filtering/component separation (sparse signal/trend/noise). The cost function contains: A quadratic data fidelity term, Some smoothed $\ell_1$ terms for ...
0
votes
1answer
53 views

Best way to approximate a curve?

I have a curve like this one: I need a function to approximate this curve, but I need that the function be a low order function (less than 5). What is a good way to obtain what I expect? Thanks!
3
votes
2answers
93 views

Convex optimization in signal processing

In signal processing, convex optimization plays a useful role in problems such as sparse signal recovery and filter design. What other places does convex optimization appear? For example, in ...
1
vote
3answers
69 views

Decomposing a DFT into multiple FFT calls

I'm using a good fast FFT implementation (vDSP) that will only work on power of 2 blocks of audio data. Now I have a problem where I would like to be able to apply the calculations to non powers of 2 ...
3
votes
0answers
122 views

Weighted Nuclear Norm Minimization for Image Denoising

Recently, I saw new published papers like this paper about denoising images using Weighted Nuclear Norm Minimization (WNNM) approach and I am wondering what is the physical intuition behind it. The ...
0
votes
0answers
20 views

Is it possible to auto compute for the optimal value of Lagrangian multiplier?

Consider the cost function $f(X,\lambda) = \|AX-b\|_2^2 + \alpha \|LX\|_2^2$ $A:$Measurement matrix($R_{m\times n}$,$m \ll n$), $b:$observation vector($R_m$), $L:$Laplacian operator($R_{n \times ...
0
votes
1answer
34 views

Significance of Lambda in Basis pursuit

In basis Pursuit, L1 minimization is done to perform compressed sensing. In the literature there is a $\lambda$ parameter used as a regulizer. What is its significance?
0
votes
1answer
77 views

Finding the gradient of a norm in a minimization problem

I have to find the gradient of the following term with respect to $X_{1}$: $\|\Phi\circ(X_{1}-X_{2})-u\|_F^2$ , where $u\in\mathbb{R}^{n}$; $X_{1}, X_{2}\in\mathbb{R}^{N\times J}$ and ...
2
votes
0answers
45 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 ...
1
vote
1answer
589 views

$l_0$ 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 $l_0$ norm ...
0
votes
1answer
55 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
46 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
118 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 ...
1
vote
0answers
90 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 ...
2
votes
0answers
97 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
votes
0answers
466 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
votes
0answers
60 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
173 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
324 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
1k 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
109 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
74 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
120 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 ...
14
votes
1answer
583 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 ...