Related papers: Sigma Delta quantization for images
Several analog-to-digital conversion methods for bandlimited signals used in applications, such as Sigma Delta quantization schemes, employ coarse quantization coupled with oversampling. The standard mathematical model for the error accrued…
In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the $\Sigma\Delta$ quantization scheme, the…
Sigma Delta quantization, a quantization method which first surfaced in the 1960s, has now been used widely in various digital products such as cameras, cell phones, radars, etc. The method samples an input signal at a rate higher than the…
In this paper, we study error diffusion techniques for digital halftoning from the perspective of 1-bit Sigma-Delta quantization. We introduce a method to generate Sigma-Delta schemes for two-dimensional signals as a weighted combination of…
In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the $\Sigma\Delta$ quantization scheme, the…
We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…
In this paper we study the quantization stage that is implicit in any compressed sensing signal acquisition paradigm. We propose using Sigma-Delta quantization and a subsequent reconstruction scheme based on convex optimization. We prove…
Sigma-Delta modulation is a popular method for analog-to-digital conversion of bandlimited signals that employs coarse quantization coupled with oversampling. The standard mathematical model for the error analysis of the method measures the…
Sampling and quantization are crucial in digital signal processing, but quantization introduces errors, particularly due to distribution mismatch between input signals and quantizers. Existing methods to reduce this error require precise…
We construct an adaptive asymptotically optimal in the classical norm of the space L(2) of square integrable functions non - parametrical multidimensional time defined signal regaining (adaptive filtration, noise canceller) on the…
Many communication-efficient variants of SGD use gradient quantization schemes. These schemes are often heuristic and fixed over the course of training. We empirically observe that the statistics of gradients of deep models change during…
This paper addresses the challenges of storage and communication costs for large-scale datasets in resource-constrained edge devices by proposing a novel dataset quantization approach to reduce intra-sample redundancy. Unlike traditional…
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. Recent advances using the distributed gradient…
We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit…
Scalar quantization is the most practical and straightforward approach to signal quantization. However, it has been shown that scalar quantization of oversampled or Compressively Sensed signals can be inefficient in terms of the…
There have been a number of studies on sparse signal recovery from one-bit quantized measurements. Nevertheless, little attention has been paid to the choice of the quantization thresholds and its impact on the signal recovery performance.…
Suppose that the collection $\{e_i\}_{i=1}^m$ forms a frame for $\R^k$, where each entry of the vector $e_i$ is a sub-Gaussian random variable. We consider expansions in such a frame, which are then quantized using a Sigma-Delta scheme. We…
Quantizing deep networks with adaptive bit-widths is a promising technique for efficient inference across many devices and resource constraints. In contrast to static methods that repeat the quantization process and train different models…
In recent years Deep Neural Networks (DNNs) have been rapidly developed in various applications, together with increasingly complex architectures. The performance gain of these DNNs generally comes with high computational costs and large…
Quantization of compressed sensing measurements is typically justified by the robust recovery results of Cand\`es, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size $\delta$ is used to quantize…