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Constrained independent component analysis (C-ICA) algorithms have been an effective way to introduce prior information into the ICA framework. The work in this area has focus on adding constraints to the objective function of algorithms that assume an orthogonal demixing matrix. Orthogonality is required in order to decouple—isolate—the constraints applied for each individual source. This assumption limits the optimization space and therefore the separation performance of C-ICA algorithms. We generalize the existing C-ICA framework by using a novel decoupling method that preserves the larger optimization space for the demixing matrix. In addition, this framework allows for the constraining of either the sources or the mixing coefficients. A constrained version of the extended Infomax algorithm is used as an example to show the benefits obtained from the non-orthogonal constrained framework we introduce. [ABSTRACT FROM PUBLISHER]

This paper presents an analysis of a fixed-point recursive least squares (RLS) algorithm for first-order Markov channel estimation and derives expressions for the mean weight misadjustment. The expressions derived are general in that they take into account the correlation in the input. It is shown that correlation amplifies the effect of roundoff error due to the desired signal estimate computation and the additive system noise. The misadjustment due to time-varying system weights and the weight update roundoff error behave similarly and are minimally affected by the input correlation. They contribute to the total misadjustment in such a way that is directly proportional to the algorithm's time constant which is a function of the algorithm forgetting factor. The contributions of system noise and roundoff error due to the desired estimate, on the other hand, are inversely proportional to the algorithm time constant. Hence, they indicate a tradeoff in the choice of the forgetting factor to balance the effects of these noise sources. We present simulation results which demonstrate very good agreement with the theory. Keywords: Fixed-point analysis; RLS algorithm; System identification; Roundoff errors; Time-varying systems; Steady-state performance; Recursive least squares algorithm; Input correlation effects

In this paper, we introduce a novel way of performing real-valued optimization in the complex domain. This framework enables a direct complex optimization technique when the cost function satisfies the Brandwood's independent analyticity condition. In particular, this technique has been used to derive three algorithms, namely, kurtosis maximization using gradient update (KM-G), kurtosis maximization using fixed-point update (KM-F), and kurtosis maximization using Newton update (KM-N), to perform the complex independent component analysis (ICA) based on the maximization of the complex kurtosis cost function. The derivation and related analysis of the three algorithms are performed in the complex domain without using any complex-real mapping for differentiation and optimization. A general complex Newton rule is also derived for developing the KM-N algorithm. The real conjugate gradient algorithm is extended to the complex domain similar to the derivation of complex Newton rule. The simulation results indicate that the fixed-point version (KM-F) and gradient version (KM-G) are superior to other similar algorithms when the sources include both circular and noncircular distributions and the dimension is relatively high. [ABSTRACT FROM AUTHOR]

Surface reconstruction is a critical step in three-dimensional image processing and understanding. In this letter, a discontinuity-embedded deformable model has been developed to model surfaces with discontinuities. Governed by the Lagrange motion equation, a finite-element representation of the model can dynamically fit the data in both continuous and discontinuous components, reaching its equilibrium in response to induced forces. Experimental results on synthetic and range images demonstrate a significant improvement in preserving depth discontinuities over conventional approaches. [ABSTRACT FROM AUTHOR]