Noisy PCA theory and application in filter bank codec design

Noisy principal component analysis (NPCA) was introduced previously as an extension of PCA in the assumption that the linear features are unreliable. The level of noise in the representation variables is found to have effects in the rank of the optimal solution resembling the water-filling analogy in information theory. The NPCA problem needs to be coupled with certain constraints so that it permits a finite solution. We present the solution of the NPCA problem under different constraints which can be useful in applications involving bandwidth limitations. One of these applications is the design of optimal subband coders incorporating quantization noise. In addition to the NPCA-optimality another advantage of the new design approach is that it works entirely in the time domain and thus the costly and difficult transformations to and from the Z-domain can be avoided.