Memoryless scalar quantization (MSQ) is a common technique to quantize generalized linear samples of signals. The non-linear nature makes the analysis corresponding approximation error challenging, often resulting in use simplifying assumption, called “white noise hypothesis” (WNH) that useful, yet also known be not rigorous and, at least certain cases, valid. We obtain reconstruction estimates...

In this paper, we propose a novel feedforward adaptive quantization scheme called the sample-adaptive product quantizer (SAPQ). This is a structurally constrained vector quantizer that uses unions of product codebooks. SAPQ is based on a concept of adaptive quantization to the varying samples of the source and is very different from traditional adaptation techniques for nonstationary sources. S...

In this report, we introduce a novel feed-forward adaptive quantization scheme called SAPQ (sampleadaptive product quantizer) as a structurally constrained vector quantizer. SAPQ is based on a concept of adaptive quantization t o the varying samples of the source and is very different, from traditional adaptation techniques for non-stationary sources. SAPQ quantizes each source sample using a s...

We have obtained optimization methods to achieve minimum distortion levels for scalar and vector quantization. Unfortunately, the optimization methods are usually expensive and long. Many simpler methods to achieve (not as good as the optimal one, but) quite good performance have been developed both for scalar and for vector quantization applications. We will list a few of these many methods here.

The principle of subband coding of images has been studied intensively for years. In our work on subband coding of images we have focused on a particular IIR lter bank structure that produces complex valued subband signals. In previously reported coders, data compression is achieved as a result of scalar quantization or vector quantization (VQ) of the encoder sub-band signals 1. In this paper w...

In the context of loop quantum cosmology, we consider an inflationary era driven by a canonical scalar field and occurring in the semiclassical regime, where spacetime is a continuum but quantum gravitational effects are important. The spectral amplitude and index of scalar perturbations on an unperturbed de Sitter background are computed at lowest order in the slow-roll parameters. The scalar ...

We consider the properties of optimal xed-rate and entropy-constrained scalar quantizers for nite alphabet sources. In particular, w econsider conditions under which the optimal scalar quantizer with contiguous codecells achieves performance no worse than the optimal scalar quantizer without the constraint of codecell contiguit y.In addition to traditional scalar quantizers, w econsider multi-r...

We consider the quantization of a massless scalar field, using the geometric optics approximation, in the background spacetime of a collapsing spherical self-similar Vaidya star, which forms a black hole or a naked singularity. We show that the outgoing radiation flux of the quantized scalar field diverges on the Cauchy horizon. The spectrum of the produced scalar partcles is non-thermal when t...