IEEE Transactions on Information Theory
A subgradient solution to structured robust least squares problems
IEEE Transactions on Signal Processing
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The least squares (LS) and total least squares (TLS) methods are commonly used to solve the overdetermined system of equations $Ax \approx b$. The main objective of this paper is to examine TLS when $A$ is nearly rank deficient by outlining its differences and similarities to the well-known truncated LS method. It is shown that TLS may be viewed as a regularization technique much like truncated LS, even though the rank reduction depends on $b$. The sensitivity of LS and TLS approximate nullspaces to perturbations in the data is also examined. Some numerical simulations are included.