Gradient Algorithm for Nonnegative Independent Component Analysis

2006 ◽  
pp. 1115-1120
Author(s):  
Shangming Yang
Keyword(s):  
Independent Component Analysis ◽  
Component Analysis ◽  
Independent Component ◽  
Gradient Algorithm

scholarly journals Blind Separation of Positive Sources by Globally Convergent Gradient Search

2004 ◽  
Vol 16 (9) ◽  
pp. 1811-1825 ◽  
Author(s):  
Erkki Oja ◽  
Mark Plumbley
Keyword(s):  
Independent Component Analysis ◽  
Cost Function ◽  
Gradient Flow ◽  
Component Analysis ◽  
Independent Component ◽  
Gradient Algorithm ◽  
Stiefel Manifold ◽  
Blind Separation ◽  
Solution Methods ◽  
Simplified Solution

The instantaneous noise-free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix. However, with some prior information on the sources, like positivity, new analysis and perhaps simplified solution methods may yet become possible. In this letter, we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded, which means that they have a nonzero pdf in the region of zero. It can be shown that in this case, the solution method is basically very simple: an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources. We propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint, under which the separating matrix is orthogonal. We further prove that in the Stiefel manifold of orthogonal matrices, the cost function is a Lyapunov function for the matrix gradient flow, implying global convergence. Thus, this algorithm is guaranteed to find the nonnegative well-grounded independent sources. The analysis is complemented by a numerical simulation, which illustrates the algorithm.

scholarly journals Improvement and Assessment of a Blind Image Deblurring Algorithm Based on Independent Component Analysis

Computation ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 76
Author(s):  
Simone Fiori
Keyword(s):  
Independent Component Analysis ◽  
Component Analysis ◽  
Image Deblurring ◽  
Independent Component ◽  
Gradient Algorithm ◽  
Gabor Filtering ◽  
Original Technique ◽  
Blind Image Deblurring ◽  
Blurred Image ◽  
Blind Image

The aim of the present paper is to improve an existing blind image deblurring algorithm, based on an independent component learning paradigm, by manifold calculus. The original technique is based on an independent component analysis algorithm applied to a set of pseudo-images obtained by Gabor-filtering a blurred image and is based on an adapt-and-project paradigm. A comparison between the original technique and the improved method shows that independent component learning on the unit hypersphere by a Riemannian-gradient algorithm outperforms the adapt-and-project strategy. A comprehensive set of numerical tests evidenced the strengths and weaknesses of the discussed deblurring technique.

Skin Chromophore Estimation from Mobile Selfie Images using Constrained Independent Component Analysis

2020 ◽  
Vol 2020 (14) ◽  
pp. 357-1-357-6
Author(s):  
Luisa F. Polanía ◽  
Raja Bala ◽  
Ankur Purwar ◽  
Paul Matts ◽  
Martin Maltz
Keyword(s):  
Independent Component Analysis ◽  
Spectral Reflectance ◽  
Source Separation ◽  
Principal Component ◽  
Component Analysis ◽  
Previous Method ◽  
Independent Component ◽  
Light Transport ◽  
Camera Model ◽  
Constrained Independent Component Analysis

Human skin is made up of two primary chromophores: melanin, the pigment in the epidermis giving skin its color; and hemoglobin, the pigment in the red blood cells of the vascular network within the dermis. The relative concentrations of these chromophores provide a vital indicator for skin health and appearance. We present a technique to automatically estimate chromophore maps from RGB images of human faces captured with mobile devices such as smartphones. The ultimate goal is to provide a diagnostic aid for individuals to monitor and improve the quality of their facial skin. A previous method approaches the problem as one of blind source separation, and applies Independent Component Analysis (ICA) in camera RGB space to estimate the chromophores. We extend this technique in two important ways. First we observe that models for light transport in skin call for source separation to be performed in log spectral reflectance coordinates rather than in RGB. Thus we transform camera RGB to a spectral reflectance space prior to applying ICA. This process involves the use of a linear camera model and Principal Component Analysis to represent skin spectral reflectance as a lowdimensional manifold. The camera model requires knowledge of the incident illuminant, which we obtain via a novel technique that uses the human lip as a calibration object. Second, we address an inherent limitation with ICA that the ordering of the separated signals is random and ambiguous. We incorporate a domain-specific prior model for human chromophore spectra as a constraint in solving ICA. Results on a dataset of mobile camera images show high quality and unambiguous recovery of chromophores.

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