This paper investigates the problem of initial phase estimation for a real-valued sinusoidal signal with known frequency. We analyze the bias of the conventional maximum likelihood estimator (MLE) and show that it primarily arises from spectral leakage in the discrete Fourier transform (DFT). Based on this observation, we propose a novel unbiased estimator that eliminates the influence of spectral leakage, thereby achieving unbiased estimation of the initial phase. From a theoretical perspective, we prove that a statistic related to the proposed unbiased estimator is not complete. As a result, it is not possible to theoretically establish that the proposed estimator is the minimum variance unbiased estimator (MVUE) within the framework of the Lehmann–Scheffé theorem, due to the incompleteness of the statistic. Nevertheless, Monte Carlo simulations are conducted to evaluate the performance of the proposed estimator under various frequencies, initial phases, and signal-to-noise ratio (SNR) conditions. The results show that the proposed method consistently achieves unbiased estimation and yields a variance close to the Cramér–Rao lower bound (CRLB) in all tested scenarios.

Point cloud semantic segmentation can enhance the understanding of the production environment and is a crucial component of vision tasks. The efficacy and generalization prowess of deep learning-based segmentation models are inherently contingent upon the quality and nature of the data employed in their training. However, it is often challenging to obtain data with inter-class balance, and training an intelligent segmentation network with the imbalanced data may cause cognitive bias. In this paper, a network framework InvSpaceNet is proposed, which generates an inverse feature space to alleviate the cognitive bias caused by imbalanced data. Specifically, we design a dual-branch training architecture that combines the superior feature representations derived from instance-balanced sampling data with the cognitive corrections introduced by the proposed inverse sampling data. In the inverse feature space of the point cloud generated by the auxiliary branch, the central points aggregated by class are constrained by the contrastive loss. To refine the class cognition in the inverse feature space, features are used to generate point cloud class prototypes through momentum update. These class prototypes from the inverse space are utilized to generate feature maps and structure maps that are aligned with the positive feature space of the main branch segmentation network. The training of the main branch is dynamically guided through gradients back propagated from different losses. Extensive experiments conducted on four large benchmarks (i.e., S3DIS, ScanNet v2, Toronto-3D, and SemanticKITTI) demonstrate that the proposed method can effectively mitigate point cloud imbalance issues and improve segmentation performance.

To significantly enhance the performance of point cloud semantic segmentation, this manuscript presents a novel method for constructing large-scale networks and offers an effective lightweighting technique. First, a latent point feature processing (LPFP) module is utilized to interconnect base networks such as PointNet++ and Point Transformer. This intermediate module serves both as a feature information transfer and a ground truth supervision function. Furthermore, in order to alleviate the increase in computational costs brought by constructing large-scale networks and better adapt to the demand for terminal deployment, a novel point cloud lightweighting method for semantic segmentation network (PCLN) is proposed to compress the network by transferring multidimensional feature information of large-scale networks. Specifically, at different stages of the large-scale network, the structure and attention information of the point features are selectively transferred to guide the compressed network to train in the direction of the large-scale network. This paper also solves the problem of representing global structure information of large-scale point clouds through feature sampling and aggregation. Extensive experiments on public datasets and real-world data demonstrate that the proposed method can significantly improve the performance of different base networks and outperform the state-of-the-art.

Newton's rings experiment is a fundamental experiment. The rings counting method has been used to reveal the phenomenon of equal-thickness interference in physics for over 100 years. This paper proposes two perspectives on observing Newton's rings. From the perspective of signal processing, fractional Fourier transform are introduced into the Newton's rings experiment to reveal the mathematical nature of the fringe. From the perspective of data analysis, the deep neural network is trained so that it can intelligently analyze Newton's rings. High precision measurement of physical parameters such as the radius of curvature of a lens can be completed directly without counting rings. These two new perspectives provide good extensions to university physics experiments, which can be followed by additional theoretical and experimental sessions to further understand Newton's rings. The new session can be added to the current physics, signal processing and artificial intelligence courses. A brand-new course is designed to help students understand recent Newton's rings processing methods and know the pros and cons of them. which broaden their horizons and stimulate their creative thinking.

The short-time fractional Fourier transform (STFRFT) has been shown to be a powerful tool for processing signals whose fractional frequencies vary with time. However, for real-time applications that require recalculating the STFRFT at each or several samples, the existing discrete algorithms are not suitable. To solve this problem, a new sliding algorithm is proposed, termed as the sliding STFRFT. First, the sliding STFRFT algorithm with the sliding step 1 is proposed. Then, it is derived to the circumstance when the sliding step turns to$\bm {p\;(p > 1)}$. The proposed sliding STFRFT algorithm directly computes the STFRFT at the time$\bm {m+1}$or$\bm {m+p}$using the STFRFT output result at the time$\bm {m}$, which greatly reduces the computation complexity. The theoretical analysis demonstrates that the proposed algorithm has the lowest computational cost among existing STFRFT algorithms.

Hyperspectral images have high spectral resolution, but this is often at the expense of spatial resolution. Although deep learning-based super-resolution (SR) algorithms have shown comparative performance for spatial resolution enhancement, most of them cannot effectively extract features of different size objects because of single scale convolution. In deep architectures, low level features also tend to disappear during transmission. In this paper, an efficient network (MRBMFF) for enhancing the spatial resolution of hyperspectral image is proposed. Based on the multiscale residual block (MRB), features at different scales can be effectively extracted and fused. Meanwhile, the multilevel feature fusion (MFF) is introduced to concatenate the low and high level features. Effective SR images could be recovered after inputting their low-resolution counterparts to the proposed network. Experimental results show that the proposed network achieves superior reconstruction performance compared with the state-of-the-art approaches.

Random Gaussian noise and striping artifacts are common phenomena in hyperspectral images (HSI). In this article, an effective restoration method is proposed to simultaneously remove Gaussian noise and stripes by merging a denoising and a destriping submodel. A denoising submodel performs a multiband denoising, i.e., Gaussian noise removal, considering Gaussian noise variations between different bands, to restore the striped HSI from the corrupted image, in which the striped HSI is constrained by a weighted nuclear norm. For the destriping submodel, we propose an adaptive anisotropy total variation method to adaptively smoothen the striped HSI, and we apply, for the first time, the truncated nuclear norm to constrain the rank of the stripes to 1. After merging the above two submodels, an ultimate image restoration model is obtained for both denoising and destriping. To solve the obtained optimization problem, the alternating direction method of multipliers (ADMM) is carefully schemed to perform an alternative and mutually constrained execution of denoising and destriping. Experiments on both synthetic and real data demonstrate the effectiveness and superiority of the proposed approach.

In communications and radar/sonar systems, one of the most popular nonstationary stochastic signal models is the chirp cyclostationary (CCS) signal. Recently, the second-order statistics of complex CCS signals are defined based on the conjugate correlation function, which have shown to be more proper in linear canonical transform domain than in the frequency domain. However, the information provided by unconjugate correlation function is missing, which leads to an incomplete study of second-order CCS signals. In this letter, the unified conjugate and unconjugate correlation function of CCS signals is researched. In detail, the definitions of the novel second-order statistics, chirp cyclic correlation and chirp cyclic spectrum, are expounded. Then the properties of these statistics are investigated. Finally, the additional information provided by the correlation function with conjugate operation and the usefulness of the proposed statistics are introduced and explained by simulations.

The two-dimensional discrete fractional Fourier transform (2D DFrFT) has been shown to be a powerful tool for 2D signal processing. However, the existing discrete algorithms aren't the optimal for real-time applications, where the input signals are stream data arriving in a sequential manner. In this letter, a new sliding algorithm is proposed to solve this problem, termed as the 2D sliding DFrFT (2D SDFrFT). The proposed 2D SDFrFT algorithm directly computes the 2D DFrFT in current window using the results of previous window, which greatly reduces the computations. During the derivation, we find that the (m + δ, n)th DFrFT bin in previous window is needed for computing the (m, n)th DFrFT bin in current window, where the increment δ isn't always an integer. Further, a method is proposed to convert the increment δ to a certain integer by determining appropriate sampling interval. The theoretical analysis demonstrates that when compute the new 2D DFrFT in a shifted window in sliding process, our proposed algorithm has the lowest computational cost among existing 2D DFrFT algorithms.

Microwave radiometers are the key sensors to globally monitor environmental parameters; however, it suffers from its low and nonuniform spatial resolution. In this paper, a superresolution (SR) technique based on image degradation and residual network is proposed to enhance the spatial resolution of microwave radiometer data. Specifically, an improved degradation model is proposed to construct pairs of high-resolution (HR) and low-resolution (LR) data for training and testing. In addition, a new residual network connected by the SR main and gradient auxiliary branches in parallel is designed to achieve SR reconstructions, where eight-channel gradient maps extracted from LR data are input into the auxiliary branch to help to reconstruct. SR results are eventually generated by the trained SR network. Experiments executed on both simulated and actual data demonstrate the soundness and the superiority of the proposed SR technique.

Multichannel sampling is fundamental in the theory of multichannel parallel analog-to-digital converters and multiplexing wireless communication. This letter investigates the multichannel consistent sampling theory associated with the linear canonical transform, which can combine the reconstruction of the signal and the correction of sensor distortions. The consistency requests that a resampling of the reconstruction by the original sampling operation yields the same measurements as before. The consistent sampling is applicable to an arbitrary finite energy signal and without the constraint such as band-limiting. Under this circumstance, two effective reconstruction methods based on the shift-invariant reconstruction space and the linear canonical basis functions space are developed. Finally, the reconstruction experiment of the radar echo signal is presented.

Signal reconstruction from non‐uniform samples, especially for non‐stationary signals, is an important issue in the area of digital signal processing. As a type of signal processing tool, the fractional Fourier transform has been proved to be effective for solving problems in non‐stationary signal processing. For non‐stationary discrete‐time signals, the reconstruction of uniformly sampled signals from non‐uniform samples in the fractional Fourier domain is first derived in this study. Since only finite non‐uniform samples are collected in practical applications, for preferable reconstruction, two types of symmetric extensions are considered in the reconstruction to overcome the discontinuity problem that exists in the periodisation of short non‐stationary sequences, which is more critical than that of long sequences. In addition, the average signal‐to‐noise ratio is used to evaluate the performance of the reconstruction with two types of symmetric extensions. Simulations and two applications are given to verify the effectiveness of the proposed reconstruction method.

Linear canonical transform (LCT), which can be deemed to be a generalisation of the fractional Fourier transform, has been used in several areas, including signal processing and optics. Motivated by the operator theory, a new unitary operator associated with the LCT is introduced. This new operator generalises the unitary fractional operator which is proposed by Akay et al . recently. Via operator manipulations, the authors also derive a new definition, the LCT correlation operation, and present an alternative and efficient implementation of it. It is shown that the proposed LCT autocorrelation corresponds to radial slices of the ambiguity function in the ambiguity plane. On the basis of this relationship, an application of the fast LCT autocorrelation for detection and parameter estimation with respect to the chirp rates of linear frequency modulated signals corrupted by noise is proposed. Finally, the validity of the proposed method is verified by simulation results.

The fractional Fourier transform (FRFT) is one of the most useful tools for the nonstationary signal processing. In this paper, the randomized nonuniform sampling and approximate reconstruction of the nonstationary random signals in the fractional Fourier domain (FRFD) are developed. The nonuniform samples are treated as random perturbations from a uniform grid. The samples used for the sinc interpolation reconstruction are placed on another nonuniform grid which is not necessarily equal to the samples originally acquired. When considering the second-order random statistic characters, the nonuniform sampling is equivalent to the uniform sampling of the signal after a pre-filter in the FRFD, where the frequency response is related to the characteristic function (with its argument scaled by csc α ) of the perturbations. The effectiveness of the reconstruction is analyzed and the mean square error (MSE) is computed by utilizing the equivalent filter system. Furthermore, the randomized reconstruction of the chirp period stationary random signal is proposed. At last, the minimum MSE on the special cases of the randomized sampling and reconstruction is discussed. The effectiveness of the proposed reconstruction method is verified by the simulation.

We propose a multichannel random discrete fractional Fourier transform (MRFrFT) with random weighting coefficients and partial transform kernel functions. First, the weighting coefficients of each channel are randomized. Then, the kernel functions, selected based on a choice scheme, are randomized using a group of random phase-only masks (RPOMs). The proposed MRFrFT can be carried out both electronically and optically, and its main features and properties have been given. Numerical simulation about one-dimensional signal demonstrates that the MRFrFT has an important feature that the magnitude and phase of its output are both random. Moreover, the MRFrFT of two-dimensional image can be viewed as a security enhanced image encryption scheme due to the large key space and the sensitivity to the private keys.