Tomosynthesis is an emerging technique with potential to replace mammography, since it gives 3D information at a relatively small increase in dose and cost. We present an analytical singular-value decomposition of a tomosynthesis system, which provides the measurement component of any given object. The method is demonstrated on an example object. The measurement component can be used as a recon...

A new approach to low-complexity channel estimation in orthogonal-frequency division multiplexing (OFDM) systems is proposed. A lowrank approximation is applied to a linear minimum mean-squared error (LMMSE) estimator that uses the frequency correlation of the channel. By using the singular-value decomposition (SVD) an optimal low-rank estimator is derived, where performance is essentially pres...

The Higher-Order SVD (HOSVD) is a generalization of the Singular Value Decomposition (SVD) to higher-order tensors (i.e. arrays with more than two indices) and plays an important role in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a third-order tensor involves the computation of the SVD of three matrices, which are referred to as "modes"...

Minimizing the rank of a matrix subject to affine constraints is a fundamental problem with many important applications in machine learning and statistics. In this paper we propose a simple and fast algorithm SVP (Singular Value Projection) for rank minimization with affine constraints (ARMP) and show that SVP recovers the minimum rank solution for affine constraints that satisfy the restricted...

A singular value inequality due to Bhatia and Kittaneh says that if A and B are compact operators on a complex separable Hilbert space such that A is self-adjoint, B 0, and A B; then sj(A) sj(B B) for j = 1; 2; :::We give an equivalent inequality, which states that if A;B; and C are compact operators such that A B B C 0; then sj(B) sj(A C) for j = 1; 2; :::Moreover, we give a sharper inequality...

The problem of outliers is well-known in statistics: an outlier is a value that is far from the general distribution of the other observed values, and can often perturb the results of a statistical analysis. Various procedures exist for identifying outliers, in case they need to receive special treatment, which in some cases can be exclusion from consideration. An inlier, by contrast, is an obs...

The tensor M has 3 = 81 entries and no symmetries. Both the construction and application of M are somewhat expensive, and both can be avoided. If F = UΣV , then it turns out that Z(F, α) = UẐ(Σ, α)V and W(F) = UŴ(Σ)V , where Ẑ(Σ, α) and Ŵ(Σ) are diagonal matrices. It follows then that Y(F) = UŶ(Σ)V , with Ŷ(Σ) = Ŵ(Ẑ(Σ, α)), where Ŷ(Σ) is also a diagonal matrix. To be able to carry out these ste...

The tensor M has 3 = 81 entries and no symmetries. Both the construction and application of M are somewhat expensive, and both can be avoided. If F = UΣV , then it turns out that Z(F, α) = UẐ(Σ, α)V and W(F) = UŴ(Σ)V , where Ẑ(Σ, α) and Ŵ(Σ) are diagonal matrices. It follows then that Y(F) = UŶ(Σ)V , with Ŷ(Σ) = Ŵ(Ẑ(Σ, α)), where Ŷ(Σ) is also a diagonal matrix. To be able to carry out these ste...

High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data analysis. Existing methods, aimed at signal reconstruction and deconvolution...

The singular value decomposition, or SVD , has been studied in the past as a tool for detecting and understanding patterns in a collection of documents. We show how the matrices produced by the SVD calculation can be interpreted, allowing us to spot patterns of characters that indicate particular topics in a corpus. A test collection, consisting of two days of AP newswire tra c, is used as a ru...