The field of Signal Processing has witnessed the strong emergence of a new technique, the Blind Signal Processing (BSP) which is based on sound theoretical foundation. An offshoot of the BSP is known as Blind Source Separation (BSS). This digital signal processing techniques have a wide and varied potential applications. The term blind is indicative of the fact that both the source signal and t...

A convexity structure satisfies the separation property 5'4 if any two disjoint convex sets extend to complementary half-spaces. This property is investigated for alignment spaces, n-ary convexities, and graphs. In particular, it is proven that a) an n-ary convexity is $4 iff every pair of disjoint polytopes with at most n vertices can be separated by complementary half spaces, and b) an interv...

This paper discusses several issues related to blind source separation in nonlinear models. Specifically, separability results show that separation in the general case is impossible, however, for specific nonlinear models the problem does have a solution. A specific set of parametric nonlinear mixtures is considered, this set has the Lie group structure. In the parameter set, a group operation ...

Comprehensive two-dimensional gas chromatography (GC x GC) offers new opportunities to develop relationships between molecular structure and retentions in the two dimensional (2D) separation space defined by the GC x GC retention in each dimension. Whereas single dimension GC provides only one retention property for a solute, and hence the specific relationship between retention and chemical pr...

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the weak separation property is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the weak separation prop...

We extend to the whole class of hyperarithmetical open sets a result from 8] on the separation property, as deened in 1], of some classes of arithmetical open sets. As we do this, we slightly generalize a result from 11] about the position of arithmetical points. We also restate founda-tional connections between language theoretic separation, test equivalence, as deened in 4] over recursive tra...

In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the efficiency of the nonlinear matching pursuit method. Under the assumption of scale separation, we show that the sparse time frequency decomposition is unique up to an error that is determined by the scale separation property of the signal. We further show that the unique decomposition can be ...

This paper approaches the problem of image denoising from an Independent Component Analysis (ICA) perspective. Considering that the pixels intensity constituting the crude images represents the useful signal corrupted with noise, we show that, a nonlinear ICA-based approach can provide a satisfactory solution to the NonLinear Blind Source Separation problem (NLBSS). SelfOrganizing Maps (SOMs) a...

The criterion used for partitioning is d-separation: a parallel between causal independency property and vertex separation in digraphs. If X, Y and Z represent the vertex subsets of two neighbouring partition regions and respectively the border between them, the d-separation criterion is used to decide if " knowing Z renders Y irrelevant to X ". It follows that diagnosis may be performed locall...

We propose a new approach to solving the problem of blind separation of BPSK signals. Using the constant modulus property of the signal, we formulate this problem as a constrained minimization problem that can be solved efficiently using an extended Newton’s method on the Stiefel manifold. Compared with the existing separation methods, the proposed method is quite robust to additive noise, achi...