Sub-sampling Operation Research Articles

COVID-19 Pneumonia Classification Based on NeuroWavelet Capsule Network.

Since it was first reported, coronavirus disease 2019, also known as COVID-19, has spread expeditiously around the globe. COVID-19 must be diagnosed as soon as possible in order to control the disease and provide proper care to patients. The chest X-ray (CXR) has been identified as a useful diagnostic tool, but the disease outbreak has put a lot of pressure on radiologists to read the scans, which could give rise to fatigue-related misdiagnosis. Automatic classification algorithms that are reliable can be extremely beneficial; however, they typically depend upon a large amount of COVID-19 data for training, which are troublesome to obtain in the nick of time. Therefore, we propose a novel method for the classification of COVID-19. Concretely, a novel neurowavelet capsule network is proposed for COVID-19 classification. To be more precise, first, we introduce a multi-resolution analysis of a discrete wavelet transform to filter noisy and inconsistent information from the CXR data in order to improve the feature extraction robustness of the network. Secondly, the discrete wavelet transform of the multi-resolution analysis also performs a sub-sampling operation in order to minimize the loss of spatial details, thereby enhancing the overall classification performance. We examined the proposed model on a public-sourced dataset of pneumonia-related illnesses, including COVID-19 confirmed cases and healthy CXR images. The proposed method achieves an accuracy of 99.6%, sensitivity of 99.2%, specificity of 99.1% and precision of 99.7%. Our approach achieves an up-to-date performance that is useful for COVID-19 screening according to the experimental results. This latest paradigm will contribute significantly in the battle against COVID-19 and other diseases.

Non-Uniform Sparse Fourier Transform and Its Applications

The fast approximation algorithm of non-uniform discrete Fourier transform (NUDFT) is an important issue in signal processing. In this paper, a novel estimation algorithm is constructed for NUDFT-II, which is the general form of the sparse Fourier transform (SFT). Firstly, we propose the cyclic convolution in the non-uniform frequency domain and derive the product and convolution theorem. Secondly, the relationship is deduced between the inverse NUDFT of a uniformly sampled sequence in the frequency domain and that of a non-uniformly sampled sequence. Then, based on the relationship and cyclic convolution, we establish a random permutation operation, a non-uniform flat window filtering operation, and a frequency subsampling operation for NUDFT-II to compress sparse signal length. Meanwhile, a method to estimate the significant frequencies' locations and values is introduced. Finally, we propose the non-uniform sparse Fourier transform (NUSFT). Simulation results demonstrate that the proposed method has low complexity in sample and runtime, and has high robustness. Furthermore, the NUSFT algorithm has been applied to signal detection and reconstruction, which shows that the required signals are obtained accurately. And the NUSFT can detect frequencies that cannot be detected by the SFT.

A 265-$\mu$ W Fractional-${N}$ Digital PLL With Seamless Automatic Switching Sub-Sampling/Sampling Feedback Path and Duty-Cycled Frequency-Locked Loop in 65-nm CMOS

This article proposes a fractional- N digital phase-locked loop (DPLL) that achieves a 265- $\mu \text{W}$ ultra-low-power operation. The proposed switching feedback can seamlessly change the DPLL from sampling operation to sub-sampling operation without disturbing the phase-locked state of the DPLL to reduce the number of building blocks that works at the oscillator frequency, leading to significant power reduction. With the reduced number of high-frequency circuits, scaling the reference frequency is fully used to reduce the power consumption of the DPLL. Together with an out-of-dead-zone detector and a duty-cycled frequency-locked loop running in the background, the switching feedback achieves robust frequency and phase acquisition at start-up and helps the sub-sampling PLL recover when large phase and frequency disturbances occur. A transformer-based stacked- $g_{m}$ oscillator is proposed to minimize the power consumption while providing the sufficient swing to drive the subsequent stages. A truncated constant-slope digital-to-time converter is proposed to improve the power efficiency while retaining good linearity. The proposed fractional- ${N}$ DPLL consumes only 265 $\mu \text{W}$ while achieving an integrated jitter of 2.8 ps and a worst case fractional spur of −52 dBc, which corresponds to a figure of merit (FOM) of −237 dB.

Attention Inspired Network: Steep learning curve in an invariant pattern recognition model

Hubel and Wiesel’s study about low areas of the visual cortex (VC) inspired deep models for invariant pattern recognition. In such models, simple and complex layers alternate local feature extraction with subsampling to add invariance to distortion or transformations. However, it was shown that to tolerate large changes between examples of the same category, the subsampling operation has to discard so much information that the model loses the capability to discriminate between categories. So, in practice, small changes are tolerated by these layers and, afterwards, a powerful classifier is introduced to do the rest. By incorporating insights from higher areas of the VC, we add to the already used retinotopic step an object-centered step which increases invariance capabilities without losing so much information. By doing so, we reduce the need for a powerful, data hungry classification layer and, thus, are able to introduce a simple classification mechanism which is based on selective attention. The resulting model is tested with an invariant pattern recognition task in the MNIST and ETL-1 datasets. We verify that the model is able to achieve better accuracies with less training examples. More specifically, on the MNIST test set, the model achieves a 100% accuracy when trained with little more than 10% of the training set.

FFAST: An Algorithm for Computing an Exactly $ k$ -Sparse DFT in $O( k\log k)$ Time

It is a well-known fact that the Discrete Fourier Transform (DFT) $ \vec {X}$ of an arbitrary $ n$ -length input signal $ \vec {x}$ , can be computed from all the $ n$ time-domain samples in $O( n\log n)$ operations via a Fast Fourier Transform (FFT) algorithm. If the spectrum $ \vec {X}$ is $ k$ -sparse (where $ k\ll n$ ), can we do better? We show that asymptotically in $ k$ and $ n$ , when $ k$ is sub-linear in $ n$ (precisely, $ k= O( n^{ \delta }$ ), where $0 \leq \delta ), and the support of the non-zero DFT coefficients is uniformly random, the fast fourier aliasing-based sparse transform (FFAST) algorithm, proposed in this paper, computes, with asymptotically high probability, the $k$ non-zero DFT coefficients of $\vec {X}$ from $O( k)$ samples of $ \vec {x}$ in $O( k\log k)$ arithmetic operations. Further, the constants in the big Oh notation for both sample and computational cost are small, e.g., when $ \delta , which essentially covers a wide range of sub-linear sparsity cases, the sample cost is less than $4 k$ . Although, in this paper we assume that the samples of the signal $ \vec {x}$ observed by the FFAST are noise-free, a noise-robust extension of the FFAST is provided in a companion (Part II) paper [1] . Our approach is based on filter-less sub-sampling of the input signal using a set of carefully chosen uniform sub-sampling patterns guided by the Chinese Remainder Theorem (CRT) . The idea is to cleverly exploit, rather than avoid, the resulting aliasing artifacts induced by sub-sampling. Specifically, the sub-sampling operation on the time-domain signal $ \vec {x}$ is designed to create aliasing patterns of the non-zero coefficients of the spectrum $ \vec {X}$ to “look like” parity-check constraints of a good erasure-correcting sparse-graph code. Next, we show that computing the sparse DFT $ \vec {X}$ is equivalent to decoding of an appropriate sparse-graph code . The sparse-graph codes further permit a fast peeling-style decoding. Consequently, the resulting DFT computation is low in both the sample and the decoding complexity. We analytically connect our proposed CRT-based aliasing framework to random sparse-graph codes, and analyze the performance of our algorithm using density evolution techniques from coding theory. We provide extensive simulation results, that are in tight agreement with our theoretical findings.

R-FFAST: A Robust Sub-Linear Time Algorithm for Computing a Sparse DFT

The fast Fourier transform is the most efficiently known way to compute the discrete Fourier transform (DFT) of an arbitrary $ n$ -length signal, and has a computational complexity of $O( n\log n)$ . If the DFT $ \vec {X}$ of the signal $ \vec {x}$ has only $k$ non-zero coefficients (where $ k ), can we do better? We addressed this question and presented a novel fast Fourier aliasing-based sparse transform (FFAST) algorithm that cleverly induces sparse-graph alias codes in the DFT domain, via a Chinese-remainder-theorem-guided sub-sampling operation in the time-domain. The induced sparse-graph alias codes are then exploited to devise a fast and iterative onion-peeling style decoder that computes $ k$ -sparse DFT of an $ n$ -length signal using only $O( k)$ time-domain samples and $O( k\log k)$ computations. In this paper, we generalize the FFAST framework by Pawar and Ramchandran to the noisy setting where the time-domain samples are corrupted by white Gaussian noise. We show that the noise-robust R-FFAST algorithm computes a $ k$ -sparse DFT of an $ n$ -length signal using $O( k\log ^{3} n)$ noise-corrupted time-domain samples in $O( k\log ^{4} n)$ complexity, i.e., sub-linear sample and time complexity . In Section IX , we provide extensive simulation results validating the empirical performance of the R-FFAST algorithm, e.g., we show that the R-FFAST algorithm computes a 50-sparse DFT of an ≈ 10 million length signal using only 4800 noisy samples with an effective signal-to-noise ratio of 5 dB. We also provide comparison of the run-time performance of several existing sparse Fourier transform implementations with that of the R-FFAST and show that it is almost 20 times faster, for comparable settings, than the state-of-the-art algorithm, while simultaneously providing better support recovery guarantees. While our theoretical results are for signals with a uniformly random support of the non-zero DFT coefficients and additive white Gaussian noise, we provide simulation results, which demonstrate that the R-FFAST algorithm performs well even for signals like magnetic resonance images, that have an approximately sparse Fourier spectrum with a non-uniform support for the dominant DFT coefficients.

Folding of Phase Noise Spectra in Charge-Pump Phase-Locked Loops Induced by Frequency Division

In charge-pump phase-locked loops (CP-PLLs), the reference signal samples the phase delay between reference and feedback signals. When a frequency divider is present in the loop, the spectrum folding of the voltage-controlled oscillator phase noise caused by the inherent subsampling operation adds a relevant contribution to the in-band output noise. This brief elaborates the discrete-time linear model of PLLs to take into account spectrum folding and provides a simple equation for the estimation of the output noise. The closed-form expressions are validated on the basis of behavioral simulations of a third-order CP-PLL.

Regularization Super-Resolution with Inaccurate Image Registration

Considering the inaccuracy of image registration, we propose a new regularization restoration algorithm to solve the ill-posed super-resolution (SR) problem. Registration error is used to obtain cross-channel error information caused by inaccurate image registration. The registration error is considered as the noise mean added into the within-channel observation noise which is known as Additive White Gaussian Noise (AWGN). Based on this consideration, two constraints are regulated pixel by pixel within the framework of Miller's regularization. Regularization parameters connect the two constraints to construct a cost function. The regularization parameters are estimated adaptively in each pixel in terms of the registration error and in each observation channel in terms of the AWGN. In the iterative implementation of the proposed algorithm, sub-sampling operation and sampling aliasing in the detector model are dealt with respectively to make the restored HR image approach the original one further. The transpose of the sub-sampling operation is implemented by nearest interpolation. Simulations show that the proposed regularization algorithm can restore HR images with much sharper edges and greater SNR improvement.