In this paper, we study the stability under convolution of the maximizing distributions of the Tsallis entropy under energy constraint (called hereafter Tsallis distributions). These distributions are shown to obey three important properties: a stochastic representation property, an orthogonal invariance property and a duality property. As a consequence of these properties, the behaviour of Tsa...

The main idea of a filter bank is to transform an input signal by subjecting it to some convolution operations, possibly followed by sampling rate reductions. We extend this idea to filter banks that are based on more general twisted convolution operations, which are not necessarily time invariant. Roughly speaking, a twisted convolution is obtained from the well-known convolution operations by...

Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alterna...

Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in ...

Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alterna...

We propose a new method for computing the 2-d Minkowski sum of non-convex polygons. Our method is convolution based. The main idea is to use the reduced convolution and filter the boundary by using the topological properties of the Minkowski sum. The main benefit of this proposed approach is from the fact that, in most cases, the complexity of the complete convolution is much higher than the co...

The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the qFT is the mismatch between the spatial and frequency domains: the convolution of two quaternion signals does not map to the pointwise product of their qFT images. The recently defined ‘Mustard’ convolution behaves ni...

This paper proposes a convolution forest kernel to effectively explore rich structured features embedded in a packed parse forest. As opposed to the convolution tree kernel, the proposed forest kernel does not have to commit to a single best parse tree, is thus able to explore very large object spaces and much more structured features embedded in a forest. This makes the proposed kernel more ro...

Convolution and Deconvolution is having wide area of application in Digital Signal Processing. Convolution helps to estimate the output of a system with arbitrary input, with knowledge of impulse response of the system. Linear systems characteristics are completely specified by the systems impulse response, as governed by the mathematics of convolution. And with the knowledge of impulse respons...