LOSoft: ℓ0 Minimization via Soft Thresholding
- Resource Type
- Conference
- Authors
- Sadeghi, Mostafa; Ghayem, Fateme; Babaie-Zadeh, Massoud; Chatterjee, Saikat; Skoglund, Mikael; Jutten, Christian
- Source
- 2019 27th European Signal Processing Conference (EUSIPCO) Signal Processing Conference (EUSIPCO), 2019 27th European. :1-5 Sep, 2019
- Subject
- Communication, Networking and Broadcast Technologies
Computing and Processing
Signal Processing and Analysis
Signal processing algorithms
Approximation algorithms
Minimization
Noise measurement
Europe
Signal processing
Iterative algorithms
Compressed sensing
sparse representation
iterative hard thresholding
iterative soft thresholding
proximal algorithms
- Language
- ISSN
- 2076-1465
We propose a new algorithm for finding sparse solution of a linear system of equations using $\ell_{0}$ minimization. The proposed algorithm relies on approximating the non-smooth $\ell_{0}$ (pseudo) norm with a differentiable function. Unlike other approaches, we utilize a particular definition of $\ell_{0}$ norm which states that the $\ell_{0}$ norm of a vector can be computed as the $\ell_{1}$ norm of its sign vector. Then, using a smooth approximation of the sign function, the problem is converted to $\ell_{1}$ minimization. This problem is solved via iterative proximal algorithms. Our simulations on both synthetic and real data demonstrate the promising performance of the proposed scheme.