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The scalar shrinkage-thresholding operator is a key ingredient in variable selection algorithms arising in wavelet denoising, JPEG2000 image compression and predictive analysis of gene microarray data. In these applications, the decision to select a scalar variable is given as the solution to a scalar sparsity penalized quadratic optimization. In some other applications, one seeks to select multidimensional...
The scalar shrinkage-thresholding operator (SSTO) is a key ingredient of many modern statistical signal processing algorithms including: sparse inverse problem solutions, wavelet denoising, and JPEG2000 image compression. In these applications, it is customary to select the threshold of the operator by solving a scalar sparsity penalized quadratic optimization. In this work, we present a natural multidimensional...
We consider the problem of linear zero forcing precoding design, and discuss its relation to the theory of generalized inverses in linear algebra. Special attention is given to a specific generalized inverse known as the pseudo-inverse. We begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudo-inverse are optimal in this setting...
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