Statistical iterative image reconstruction methods are compute intensive. Fixed-point calculations can substantially reduce the computational load, but also increase quantization error. To investigate the effect of fixed-point quantization, we analyze the error propagation after introducing perturbation in a diagonally preconditioned gradient descent algorithm for X-ray computed tomography. The...

| The nonlinear recursive di erence equations of second order bandpass Delta-Sigma modulator with sinusoidal inputs are solved. The results indicate that quantization error is neither uniformly distributed nor white. The autocorrelation of quantization error is symmetric but does not vanish as correlation index increased. The study of crosscorrelation between quantization error and sinusoidal i...

Redundant systems such as frames are often used to represent a signal for error correction, denoising and general robustness. In the digital domain quantization needs to be performed. Given the redundancy, the distribution of quantization errors can be rather complex. In this paper we study quantization error for a signal X in R represented by a frame using a lattice quantizer. We completely ch...

The performance of distributed source coding methods based on scalar quantization followed by scalar entropy coding is investigated. For a fixed quantizer, the problem is converted to that of zero-error entropy coding for bipartite graphs with a special structure. It is then experimentally shown that for bipartite graphs corresponding to jointly Gaussian sources and high-resolution uniform quan...

Many image compression standards (JPEG, MPEG, H.261) are based on the Discrete Cosine Transform (DCT). However, these standards do not specify the actual DCT quantization matrix. We have previously provided mathematical formulae to compute a perceptually lossless quantization matrix. Here I show how to compute a matrix that is optimized for a particular image. The method treats each DCT coeffic...

In this paper we propose a method for computing JPEG quantization matrices for a given mean square error or PSNR. Then, we employ our method to compute JPEG standard progressive operation mode definition scripts using a quantization approach. Therefore, it is no longer necessary to use a trial and error procedure to obtain a desired PSNR and/or definition script, reducing cost. Firstly, we esta...

In this paper, the problem of optimal quantization is solved for uniform distributions on some higher dimensional, not necessarily self-similar N−adic Cantor-like sets. The optimal codebooks are determined and the optimal quantization error is calculated. The existence of the quantization dimension is characterized and it is shown that the quantization coefficient does not exist. The special ca...

Quantization naturally exposes knobs in hardware to trade fidelity for efficiency: the more bits that are used to represent the data, the higher the storage and computation overheads. With the emergence of approximate computing research, we set out to answer the following question: how effective is quantization in trading off quality for efficiency, and how does it compare with other approximat...

Abstract To alleviate the practical constraints for deploying deep neural networks (DNNs) on edge devices, quantization is widely regarded as one promising technique. It reduces resource requirements computational power and storage space by quantizing weights and/or activation tensors of a DNN into lower bit-width fixed-point numbers, resulting in quantized (QNNs). While it has been empirically...