A Study on Sparse Signal Reconstruction from Interlaced Samples by l1-Norm Minimization
نویسنده
چکیده
We propose a sparse signal reconstruction algorithm from interlaced samples with unknown offset parameters based on the l1-norm minimization principle. A typical application of the problem is superresolution from multiple lowresolution images. The algorithm first minimizes the l1norm of a vector that satisfies data constraint with the offset parameters fixed. Second, the minimum value is further minimized with respect to the parameters. Even though this is a heuristic approach, the computer simulations show that the proposed algorithm perfectly reconstructs sparse signals without failure when the reconstruction functions are polynomials and with more than 99% probability for large dimensional signals when the reconstruction functions are Fourier cosine basis functions.
منابع مشابه
Quality index for detecting reconstruction errors without knowing the signal in l0-norm Compressed Sensing
INTRODUCTION: Compressed Sensing (CS) ([1], [2], [3], [4]) is a recently created algorithm which allows reconstructing a signal from a small portion of its Fourier coefficients if that signal is sparse in a suitable basis. It was first used by Lustig et al. [5] in MRI, and it has become a popular alternative for speeding up the MRI acquisition processes. In practice, CS has been implemented as ...
متن کاملLow-dose CT reconstruction via L1 dictionary learning regularization using iteratively reweighted least-squares
BACKGROUND In order to reduce the radiation dose of CT (computed tomography), compressed sensing theory has been a hot topic since it provides the possibility of a high quality recovery from the sparse sampling data. Recently, the algorithm based on DL (dictionary learning) was developed to deal with the sparse CT reconstruction problem. However, the existing DL algorithm focuses on the minimiz...
متن کاملSparse and Robust Signal Reconstruction
Many problems in signal processing and statistical inference are based on finding a sparse solution to an undetermined linear system. The reference approach to this problem of finding sparse signal representations, on overcomplete dictionaries, leads to convex unconstrained optimization problems, with a quadratic term l2, for the adjustment to the observed signal, and a coefficient vector l1-no...
متن کاملHomotopic l0 minimization technique applied to dynamic cardiac MR imaging
Introduction: The l1 minimization technique has been empirically demonstrated to exactly recover an S-sparse signal with about 3S-5S measurements [1]. In order to get exact reconstruction with smaller number of measurements, recently, for static images, Trzasko [2] has proposed homotopic l0 minimization technique. Instead of minimizing the l0 norm which achieves best possible theoretical bound ...
متن کاملA Hybrid L0-L1 Minimization Algorithm for Compressed Sensing MRI
INTRODUCTION Both L1 minimization [1] and homotopic L0 minimization [2] techniques have shown success in compressed-sensing MRI reconstruction using reduced k-space data. L1 minimization algorithm is known to usually shrink the magnitude of reconstructions especially for larger coefficients [1, 3] and non-convex penalty used in homotopic L0 minimization is advocated to replace L1 penalty [3]. H...
متن کامل