- 标题
- 摘要
- 关键词
- 实验方案
- 产品
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Multiple Input Single Output Phase Retrieval
摘要： In this paper, we consider the problem of recovering the phase information of multiple sources from a mixed phaseless short-time Fourier transform measurement, which is called multiple input single output (MISO) phase retrieval problem. It is an inherently ill-posed problem due to the lack of the phase and mixing information, and the existing phase retrieval algorithms are not explicitly designed for this case. To address the MISO phase retrieval problem, a least-squares method coupled with an independent component analysis (ICA) algorithm is proposed for the case of sufficiently long window length. When these conditions are not met, an integrated algorithm is presented, which combines a gradient descent algorithm by minimizing a non-convex loss function with an ICA algorithm. Experimental evaluation has been conducted to show that under appropriate conditions the proposed algorithms can explicitly recover the signals, the phases of the signals, and the mixing matrix. In addition, the algorithm is robust to noise.
关键词： Short-time Fourier transform (STFT),Multiple input single output (MISO),Independent component analysis (ICA),Non-convex optimization,Phase retrieval
更新于2025-09-19 17:15:36
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Optimization-based AMP for Phase Retrieval: The Impact of Initialization and ?2-regularization
摘要： We consider an (cid:96)2-regularized non-convex optimization problem for recovering signals from their noisy phaseless observations. We design and study the performance of a message passing algorithm that aims to solve this optimization problem. We consider the asymptotic setting m, n → ∞, m/n → δ and obtain sharp performance bounds, where m is the number of measurements and n is the signal dimension. We show that for complex signals the algorithm can perform accurate recovery with only m = (cid:0) 64 π2 ? 4(cid:1) n ≈ 2.5n measurements. Also, we provide sharp analysis on the sensitivity of the algorithm to noise. We highlight the following facts about our message passing algorithm: (i) Adding (cid:96)2 regularization to the non-convex loss function can be beneficial. (ii) Spectral initialization has marginal impact on the performance of the algorithm. The sharp analyses in this paper, not only enable us to compare the performance of our method with other phase recovery schemes, but also shed light on designing better iterative algorithms for other non-convex optimization problems.
关键词： (cid:96)2-regularization,spectral initialization,Phase retrieval,approximate message passing,non-convex optimization
更新于2025-09-19 17:15:36
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[IEEE 2018 IEEE Fourth International Conference on Multimedia Big Data (BigMM) - Xi'an (2018.9.13-2018.9.16)] 2018 IEEE Fourth International Conference on Multimedia Big Data (BigMM) - Adaptive Optimization with Nested Prior Navigation for Blind Image Deblurring
摘要： Image deblurring is a typical inverse problem and has many applications in vision and multimedia areas. It involves the estimation of blur kernel and sharp image given only a blurry observation. Due to the fundamentally ill-posed nature, most existing works design different priors within the maximum a posteriori (MAP) framework to regularize their solution space. However, due to the unknown image distribution, complex kernel structure and non-uniform noises, it is indeed challenging to explicitly design a fixed prior for blurry images in real-world scenarios. Different from these conventional strategies to integrate sophisticated priors into optimization model, this work only formulates the necessary constraints on latent image and blur kernel as a lightweight MAP model. Then we develop an inexact projected gradient scheme to incorporate flexible sparse structure control for MAP inference. We demonstrate that this adaptive scheme can successfully avoid degenerate solutions and is universally suitable for different blurry scenarios, such as low-illumination, face and text. Extensive experiments on both synthetic data and real-world images demonstrate the effectiveness and robustness of the proposed method against other state-of-the-art methods.
关键词： maximum a posteriori,Image deblurring,adaptive prior,non-convex optimization
更新于2025-09-10 09:29:36
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Griffin-Lim Like Phase Recovery via Alternating Direction Method of Multipliers
摘要： Recovering a signal from its amplitude spectrogram, or phase recovery, exhibits many applications in acoustic signal processing. When only an amplitude spectrogram is available and no explicit information is given for the phases, the Grif?n–Lim algorithm (GLA) is one of the most utilized methods for phase recovery. However, GLA often requires many iterations and results in low perceptual quality in some cases. In this paper, we propose two novel algorithms based on GLA and the alternating direction method of multipliers (ADMM) for better recovery with fewer iteration. Some interpretation of the existing methods and their relation to the proposed method are also provided. Evaluations are performed with both objective measure and subjective test.
关键词： STFT-based speech synthesis,spectrogram consistency,short-time Fourier transform (STFT),Non-convex optimization,phaseless spectrogram inversion
更新于2025-09-09 09:28:46
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Directional Sinogram Inpainting for Limited Angle Tomography
摘要： In this paper we propose a new joint model for the reconstruction of tomography data under limited angle sampling regimes. In many applications of Tomography, e.g. Electron Microscopy and Mammography, physical limitations on acquisition lead to regions of data which cannot be sampled. Depending on the severity of the restriction, reconstructions can contain severe, characteristic, artefacts. Our model aims to address these artefacts by inpainting the missing data simultaneously with the reconstruction. Numerically, this problem naturally evolves to require the minimisation of a non-convex and non-smooth functional so we review recent work in this topic and extend results to fit an alternating (block) descent framework. We perform numerical experiments on two synthetic datasets and one Electron Microscopy dataset. Our results show consistently that the joint inpainting and reconstruction framework can recover cleaner and more accurate structural information than the current state of the art methods.
关键词： Joint Model,Electron Microscopy,Limited Angle Tomography,Non-convex Optimization,Directional Sinogram Inpainting
更新于2025-09-09 09:28:46
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[IEEE 2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM) - Sheffield (2018.7.8-2018.7.11)] 2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM) - New Theory for Unmixing ILL-Conditioned Hyperspectral Mixtures
摘要： Hyperspectral unmixing (HU), a blind source separation problem, aims at unambiguiously identifying the spectral signatures of the materials, as well as their abundances, from the measured hyperspectral mixtures. In real hyperspectral scenes, high correlation between the spectral signatures is commonly observed, making HU quite challenging. Although such ill-conditioning is critical for effective HU, it is often ignored in existing HU literature. To the best of our knowledge, existing preconditioning techniques, for reducing the condition number of the signature matrix, were developed based on the pure-pixel assumption, which can, however, be seriously violated in remote sensing. Under a relaxed purity assumption, with respect to the pure-pixel one, this paper proposes novel theory for unmixing ill-conditioned hyperspectral mixtures. Specifically, we exactly identify the John’s ellipsoid (i.e., the maximum ellipsoid inscribed in the convex hull of the hyperspectral data vectors) via split augmented Lagrangian shrinkage algorithm (SALSA), and transform this ellipsoid into an Euclidean ball. This transformation brings the data vectors into a new space wherein the corresponding material signature vectors form a regular simplex, which is a very strong prior information. Based on this prior, we design an HU criterion, and prove its perfect identifiability under a very mild sufficient condition. Then, we demonstrate the feasibility of realizing our criterion via non-convex optimization and guarantee a stationary point solution.
关键词： split augmented Lagrangian shrinkage algorithm,Hyperspectral unmixing,pure-pixel assumption,non-convex optimization,John’s ellipsoid
更新于2025-09-09 09:28:46