压缩感知理论指出，只要信号是可压缩的或稀疏的，就能以较低的频率采样信号，并能高概率的重构该信号。在实际的应用中，许多信号只能在某些框架下具有稀疏表示，而无法在正交基下获得稀疏表示。针对这一类信号的恢复，一般采取的是l1－analysis方法。近期有些相关研究考虑了一般对偶框架下基于l1－analysis方法的信号恢复问题，在比前期l1－analysis方法更弱的条件下得到了更好的恢复结果。受此启发，我们考虑了一般对偶框架下，基于lp（0＜p≤1）最小化的信号恢复。对现有的工作做了理论推广。%The theory of compressed sensing points out that, sparse ( or compressible) signals can be re-constructed with high probability by lower sampling frequency.In more and more practical applications, many signals are sparse or approximately sparse in terms of some frames rather than orthonormal bases.In such settings, one approach to recover the signals is known as l1 -analysis.Some recent study using alter-native dual frames as analysis operators, and provide a weaker condition than existing results in the litera-ture.Inspired by this, the recovery of such kind of signals with general dual frame via lp -minimization (0≤1) is studied.The existing work in theory is extended.
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