Nonuniform recovery of fusion frame structured sparse signals

作者：Xia, Yu; Li, Song^*

来源：Analysis and Applications, 2017, 15(3): 333-352.

DOI：10.1142/S0219530516500032

• Compressed Sensing
• block sparsity
• fusion frame
• Fourier transform
• incoherence parameter
• sparse recovery

This paper considers the nonuniform sparse recovery of block signals in a fusion frame, which is a collection of subspaces that provides redundant representation of signal spaces. Combined with specific fusion frame, the sensing mechanism selects block-vector-valued measurements independently at random from a probability distribution F. If the probability distribution F obeys a simple incoherence property and an isotropy property, we can faithfully recover approximately block sparse signals via mixed l(1)/l(2)-minimization in ways similar to Compressed Sensing. The number of measurements is significantly reduced by a priori knowledge of a certain incoherence parameter lambda associated with the angles between the fusion frame subspaces. As an example, the paper shows that an s-sparse block signal can be exactly recovered from about (lambda s + 1) log(Nk) Fourier coefficients combined with fusion frame {W-j}(j=1)(N), where dim(W-j) = k.

• 出版日期2017-5
• 单位浙江大学