Questions tagged [convex-optimization]
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0
votes
1answer
72 views
Constrained LASSO Problem - $ {L}_{1} $ Regularized Least Squares with Linear Equality Constraints
I have an optimization question.
I want to solve the following problem:
$$
\arg\min_S\frac{1}{2}\|s-c\|_2^2 +\lambda\|\Phi s\|_1 \mbox{ s.t. } As = 0
$$
in which $\Phi$ is the wavelet transform ...
0
votes
1answer
45 views
Wireless Body Area Networks with Minimum Energy Consumption [closed]
For adaptive compressive sensing(cs),the sensing matrix is related to the input signal.
For example, in rakeness-based(cs), the sensing matrix is obtained by solving an optimization problem which ...
1
vote
1answer
103 views
Fast Optimization for Long FIR Filters
I need FIR filter lengths in the order of 1e4 and above to obtain reasonable accuracy in desired frequency response. The problem is that optimisation in MATLAB (e.g. fircls or the Optimization Toolbox)...
1
vote
1answer
27 views
How to Formulate a Constraint Which Ensures All Variables Have the Same Sign
I'm trying to include a constraint in my problem (to be solved by any convex optimization solver). Let {a,b,c,d ...} be a finite set of continuous variables. How to formulate a constraint which ensure ...
0
votes
1answer
48 views
The Gradient Operator of a Vectorized Image in Matrix Form
I have this optimization problem:
$$ \arg \min_{ X \left( i, j \right) } \sum_{i, j} \left\| X \left( i, j \right) - 255 \right\|_{2}^{2} + \lambda \sum_{i, j} \left\| \nabla X \left( i, j \right) - \...
1
vote
1answer
111 views
Automatic Image Enhancement of Images of Scanned Documents (Auto Whitening)
Dropbox have make a blog post about there automatic enhancement method for scanned document image - Fast Document Rectification and Enhancement.
I followed the post and they mention a formula to make ...
0
votes
2answers
89 views
Solving LASSO ($ {L}_{1} $ Regularized Least Squares) with Gradient Descent
To the best of my knowledge, state of the art methods for optimizing the LASSO objective function include the LARS algorithm and proximal gradient methods.
I was wondering however, if the LASSO ...
0
votes
2answers
335 views
Why Do Most of The Papers Use the Frobenius Norm for Denoising?
I have an noisy image and I want to remove noise from it; suppose $y$ is noisy image and $A$ is linear mask which makes my image noisy and $x$ is original image, so we have
$$
Ax + \eta = y
$$
and $\...
4
votes
1answer
414 views
How Can I Use MATLAB to Solve a Total Variation Denoising Problem?
The Total Variation Denoising Problem is given by:
$$ \arg \min_{x} \frac{1}{2} {\left\| A x - y \right\|}_{2}^{2} + \lambda \operatorname{TV} \left( x \right) $$
Where $ $ is the Total Variation ...
2
votes
1answer
106 views
Adaptive Filter Gradient Descent
The quadratic performance surface of an adaptive filter is a paraboloid. Its minimum can be found wherever the gradient is zero. However, since there are two types of paraboloids (elliptical and ...
0
votes
1answer
48 views
Regularized Least Squares by Laplacian Operator - Optimal Value of the Regularization Factor (Lagrangian Multiplier)
Consider the cost function
$$f(X,\lambda) = \|AX-b\|_2^2 + \alpha \|LX\|_2^2$$
$A:$Measurement matrix($R_{m\times n}$,$m \ll n$), $b:$observation vector($R_m$), $L:$Laplacian operator($R_{n \times n}...
0
votes
2answers
216 views
Significance of $ \lambda $ in Basis Pursuit
In basis Pursuit, L1 minimization is done to perform compressed sensing. In the literature there is a $ \lambda $ parameter used as a regularizer.
What is its significance?
3
votes
1answer
190 views
Least Angle Regression (LARS) without Matrix Inversion
Sorry if this is too damned long. I did what I could to abbreviate it.
The question is about Least Angle Regression (LARS).
I'm new to numerical work with matrices.
I believe I have a way to ...
5
votes
1answer
124 views
Ideas on Matrix Factorization / Transformations for $ {L}_{1} $ Minimization
I am starting with a typical $\ell_1$ basis pursuit problem:
$$
\min_{\mathbf{x}} \Vert \mathbf{x} \Vert_1 \quad \mathrm{s.t.} \quad \Vert \mathbf{ERx} - \mathbf{y} \Vert_2 \leq \epsilon,
$$
where $\...
7
votes
4answers
498 views
Solving Convex Optimization Problem Used for High Quality Denoising
The highest voted answer to this question suggests that to denoise a signal while preserving sharp transitions one should
minimize the objective function:
$$ |x-y|^2 + b|f(y)| $$
where $...
