High performance ℓ₁-minimization solvers
Project description
import sparsesolvers as ss
import numpy as np
N = 10
# Create an example sensing matrix
A = np.random.normal(loc=0.025, scale=0.025, size=(N, N)) + np.identity(N)
# An incoming signal
signal = np.zeros(N)
signal[2] = 1
# Use the homotopy solver to produce sparse solution, x.
x, info = ss.Homotopy(A).solve(signal, tolerance=0.1)
# Example output: error=0.064195, sparsity=0.9, argmax=2
print("error=%f, sparsity=%f, argmax=%i" % (
info.solution_error, 1 - np.count_nonzero(x) / np.double(N),
np.argmax(x)))References
A. Y. Yang, Z. Zhou, A. Ganesh, S. S. Sastry, and Y. Ma – Fast ℓ₁-minimization Algorithms For Robust Face Recognition – IEEE Trans. Image Processing, vol. 22, pp. 3234–3246, Aug 2013.
R. Chartrand, W. Yin – Iteratively Reweighted Algorithms For Compressive Sensing – Acoustics Speech and Signal Processing 2008. ICASSP 2008. IEEE International Conference, pp. 3869-3872, March 2008.
D. O’Leary – Robust Regression Computation Using Iteratively Reweighted Least Squares – Society for Industrial and Applied Mathematics, 1990
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