论文标题
关于稀疏数据恢复中拉索最小化器的稀疏性
On the sparsity of LASSO minimizers in sparse data recovery
论文作者
论文摘要
我们对不受约束的$ \ ell_1 $加权方法进行了详细分析，用于通过随机生成的矩阵从其观察中恢复稀疏数据，以满足常数$Δ<1 $的限制等轴测特性（RIP），并受到可忽略不计的测量和可压缩性错误。我们证明，如果数据为$ k $ -sparse，则套件最小化器的支持大小，$ s $，保持可比的稀疏性，$ s \ s \ leqc_Δk$。例如，如果$δ= 0.7 $，则$ s <11k $，$δ= 0.4 $ $ s $ s <4k $。我们还得出了新的$ \ ell_2/ \ ell_1 $错误界限，该限制突出了对$ k $和套索参数$λ$的精确依赖性，然后在错误驱动到可忽略不计的测量/和压缩式错误的规模之前。
We present a detailed analysis of the unconstrained $\ell_1$-weighted LASSO method for recovery of sparse data from its observation by randomly generated matrices, satisfying the Restricted Isometry Property (RIP) with constant $δ<1$, and subject to negligible measurement and compressibility errors. We prove that if the data is $k$-sparse, then the size of support of the LASSO minimizer, $s$, maintains a comparable sparsity, $s\leq C_δk$. For example, if $δ=0.7$ then $s< 11k$ and a slightly smaller $δ=0.4$ yields $s< 4k$. We also derive new $\ell_2/\ell_1$ error bounds which highlight precise dependence on $k$ and on the LASSO parameter $λ$, before the error is driven below the scale of negligible measurement/ and compressiblity errors.
