Compressed sensing (CS) theory asserts that sparse or compressible signals can be reconstructed from far fewer samples/measurements than traditional methods. A huge effort in this filed is made to ensure that the reconstruction errors with CS algorithms can stay under control. In this talk, (i) introduction to data reconstruction algorithms will be given, and some traditional and mainstream stability conditions will be briefly discussed; (ii) the advanced development of the stability theory for convex reconstruction algorithms, including the standard L1-minimization, LASSO and the Dantzig selector, will be discussed. This new development is developed through the newly introduced notion of sensing matrix with weak range space property.
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