Random Paraunitary Projections
Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through transposes in order to facilitate iterative reconstruction. We derive an efficient method to implement random unitary matrices of larger sizes through a set of Givens rotations. Random angles are hierarchically generated on-the-fly and the inverse merely requires traversing the angles in reverse order. Hierarchical randomization of angles also enables reduced storage. Using the random unitary matrices as building blocks we introduce random paraunitary systems (filter banks). We also highlight an efficient implementation of the paraunitary system and of its inverse. We also derive an adaptive under-decimated system, wherein one can control and adapt the amount of projections the signal undergoes, in effect, varying the sampling compression ratio as we go along the signal, without segmenting it. It may locally range from very compressive sampling matrices to (para) unitary random ones. One idea is to adapt to local sparseness characteristics of non-stationary signals.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Scaling-up Diverse Orthogonal Convolutional Networks with a Paraunitary Framework
Enforcing orthogonality in neural networks is an antidote for gradient vanishing/exploding problems, sensitivity by adversarial perturbation, and bounding generalization errors. However, many previous approaches are heur…
Scaling-up Diverse Orthogonal Convolutional Networks by a Paraunitary Framework
Enforcing orthogonality in neural networks is an antidote for gradient vanishing/exploding problems, sensitivity to adversarial perturbation, and bounding generalization errors. However, many previous approaches are heur…
Tight Variational Bounds via Random Projections and I-Projections
Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there…
Variational InferenceJohnson-Lindenstrauss Lemma, Linear and Nonlinear Random Projections, Random Fourier Features, and Random Kitchen Sinks: Tutorial and Survey
This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its correctness by JL lemma and its proof. …
Dimensionality ReductionLEMMARandom projections: data perturbation for classification problems
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each …
ClassificationGeneral Classification