In this paper, an FIR filter design based on total least squares error criterion is investigated. The filter coefficients are obtained from the elements of the eigenvector corresponding to minimum eigenvalue of a real, symmetric and positive definite matrix. This design is not only optimal in total least squares error sense, it is also easy to incorporate linear constraints in time and frequenc...

Sparse representations techniques have become an active domain of research in signal processing with numerous applications in compression and coding, for instance. They are mostly based on a combined `2 − `1 criterion, where the least-squares-part ensures closeness to the observations and the `1-part sparsity. We replace the least-square-part by a `∞-part and investigate the recovery conditions...

Abstract—It is well known that the Analytic Hierarchy Process (AHP) of Saaty is one of the most powerful approach for decision aid in solving of a multi criteria decision making (MCDM) problem. Several computing weights methods in AHP are analyzed. Based on least square method, three methods for calculating weights using the least the sum of squares of error criterion, the least the sum of erro...

Model selection by the predictive least squares (PLS) principle has been thoroughly studied in the context of regression model selection and autoregressive (AR) model order estimation. We introduce a new criterion based on sequentially minimized squared deviations, which are smaller than both the usual least squares and the squared prediction errors used in PLS. We also prove that our criterion...

The least squares (LS) estimation criterion on one hand, and the total LS (TLS), constrained TLS (CTLS) and structured TLS (STLS) criteria on the other hand, can be viewed as opposite limiting cases of a more general criterion, which we term “Extended LS” (XLS). The XLS criterion distinguishes measurement errors from modeling errors by properly weighting and balancing the two error sources. In ...

The aim of physical sciences is to discover the minimal set of parameters which completely describe physical systems and the laws relating the values of these parameters to the results of any set of measurements on the system. A coherent set of such laws is named a physical theory. To the extent that the values of the parameters can only be obtained as a results of measurements, one may equival...

It is shown that, in comparison to the results obtained from a conventional least squares approach, a total least squares solution leads to significant improvements in the geometry and appearance of images synthesised in a linear combination of views procedure. Use of the total least squares criterion is appropriate when errors on the control points are independently and identically distributed...

This paper deals with the problem of multivariate affine regression in the presence of outliers in the data. The method discussed is based on weighted orthogonal least squares. The weights associated with the data satisfy a suitable optimality criterion and are computed by a two-step algorithm requiring a RANSAC step and a gradient-based optimization step. Issues related to the breakdown point ...