A Study on Sparse Signal Reconstruction from Interlaced Samples by l1-Norm Minimization

نویسنده

  • Akira Hirabayashi
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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

Low-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 کامل

Sparse 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 کامل

Homotopic 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 کامل

A 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

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010