It is now well understood that (1) it is possible to reconstruct sparse
signals exactly from what appear to be highly incomplete sets of linear
measurements and (2) that this can be done by constrained L1 minimization. In
this paper, we study a novel method for sparse signal recovery that in many
situations outperforms L1 minimization in the sense that substantially fewer
measurements are needed for exact recovery. The algorithm consists of solving a
sequence of weighted L1-minimization problems where the weights used for the
next iteration are computed from the value of the current solution. We present
a series of experiments demonstrating the remarkable performance and broad
applicability of this algorithm in the areas of sparse signal recovery,
statistical estimation, error correction and image processing. Interestingly,
superior gains are also achieved when our method is applied to recover signals
with assumed near-sparsity in overcomplete representations--not by reweighting
the L1 norm of the coefficient sequence as is common, but by reweighting the L1
norm of the transformed object. An immediate consequence is the possibility of
highly efficient data acquisition protocols by improving on a technique known
as compressed sensing.

本文研究了一种新的稀疏信号恢复方法，其中加权 L1 最小化，优于传统的 L1 最小化，能够在稀疏信号恢复，图像处理和数据获得协议等领域中取得出色的性能表现。