1-bit compressing sensing (CS) is an important class of sparse optimization problems. This paper focuses on the stability theory for 1-bit CS with quadratic constraint. The model is rebuilt by reformulating sign measurements by linear equality and inequality constraints, and the quadratic constraint with noise is approximated by polytopes to any level of accuracy. A new concept called restricted weak RSP of a transposed sensing matrix with respect to the measurement vector is introduced. Our results show that this concept is a sufficient and necessary condition for the stability of 1-bit CS without noise and is a sufficient condition if the noise is available.

中文翻译：

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稀疏数据重构中1位压缩感知的稳定性

1位压缩感知（CS）是一类重要的稀疏优化问题。本文重点讨论具有二次约束的1位CS的稳定性理论。通过用线性等式和不等式约束对符号测量值进行重构来重建该模型，并且带有噪声的二次约束由多面体近似到任何精度水平。引入了一种新概念，即相对于测量矢量的转置传感矩阵的受限弱RSP。我们的结果表明，该概念对于1位CS的无噪声稳定性是充分必要的条件，并且在存在噪声的情况下也是充分条件。