Sharpness conditions directly control the recovery performance of restart schemes for first-order optimization methods without the need for restrictive assumptions such as strong convexity. However, they are challengi...
详细信息
Sharpness conditions directly control the recovery performance of restart schemes for first-order optimization methods without the need for restrictive assumptions such as strong convexity. However, they are challenging to apply in the presence of noise or approximate model classes (e.g., approximate sparsity). We provide a first-order method: weighted, accelerated, and restarted primal-dual (WARPd), based on primal-dual iterations and a novel restart-reweight scheme. Under a generic approximate sharpness condition, WARPd achieves stable linear convergence to the desired vector. Many problems of interest fit into this framework. For example, we analyze sparse recovery in com parallel to Bx parallel to l1 under constraints (l1-analysis problems for general B), and mixed regularization problems. We show how several quantities controlling recovery performance also provide explicit approximate sharpness constants. Numerical experiments show that WARPd compares favorably with specialized state-of-the-art methods and is ideally suited for solving large-scale problems. We also present a noise-blind variant based on a square-root LASSO decoder. Finally, we show how to unroll WARPd as neural networks. This approximation theory result provides lower bounds for stable and accurate neural networks for inverse problems and sheds light on architecture choices. Code and a gallery of examples are available online as a MATLAB package.
Underdetermined blind source separation has re-ceived increasing attention in recent years as an ef-fective method for speech-signal processing. Hence, a self-organizing mapping-density peak clustering and compressed ...
详细信息
Underdetermined blind source separation has re-ceived increasing attention in recent years as an ef-fective method for speech-signal processing. Hence, a self-organizing mapping-density peak clustering and compressedsensing approach, which is a two-step ap-proach, is proposed herein to improve the accuracy of underdetermined blind source separation. The ap-proach features the following two aspects: (1) A mix-ing matrix estimation method based on self-organizing mapping and density peak clustering, which can in-tuitively determine the number of source signals, re-move outliers, and determine the column vector of the mixing matrix based on local density;(2) a com-pressed sensing-based source signal reconstruction method, which can exploit the sparsity of signals in the frequency domain and use a hierarchical coupling method to reconstruct the source signal accurately and efficiently under the premise that the prior knowl-edge of the signal is unknown. The proposed method does not require the number of source signals and exhibits excellent performance under different noise conditions. Theoretical analysis and experimental re-sults demonstrate the effectiveness of the proposed method.
This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is ...
详细信息
This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is the restricted isometry constant （RIC）. Some papers provided the upper bounds of RIC to guarantee that the nuclear-norm minimization stably recovers a low-rank matrix. For example, Fazel improved the upper bounds to δ4Ar 〈 0.558 and δ3rA 〈 0.4721, respectively. Recently, the upper bounds of RIC can be improved to δ2rA 〈 0.307. In fact, by using some methods, the upper bounds of RIC can be improved to δ2tA 〈 0.4931 and δrA 〈 0.309. In this paper, we focus on the lower bounds of RIC, we show that there exists linear maps A with δ2rA 〉1√2 or δrA 〉 1/3 for which nuclear norm recovery fail on some matrix with rank at most r. These results indicate that there is only a little limited room for improving the upper bounds for δ2rA and δ***, we also discuss the upper bound of restricted isometry constant associated with linear maps A for Schatten p （0 〈 p 〈 1） quasi norm minimization problem.
A novel compressed-sensing-based(CS-based)Distributed Video Coding(DVC)system,called Distributed Adaptive compressed Video sensing(DISACOS),is proposed in this *** this system,the input frames are divided into key fra...
详细信息
A novel compressed-sensing-based(CS-based)Distributed Video Coding(DVC)system,called Distributed Adaptive compressed Video sensing(DISACOS),is proposed in this *** this system,the input frames are divided into key frames and non-key frames,which are encoded by block CS *** key frames are encoded as CS measurements at substantially higher rates than the non-key frames and decoded by the Smoothed Projected Landweber(SPL)algorithm using multi-hypothesis *** the non-key frames,a small number of CS measurements are first transmitted to detect blocks having low-quality Side Information(SI)generated by the conventional interpolation or extrapolation at the decoder;then,another group of CS measurements are sampled again upon the decoder’s *** fully utilise the CS measurements,we adaptively allocate these measurements to each block in terms of different edge ***,the residual frame is reconstructed using the SPL algorithm and the decoded non-key frame is simply determined as the sum of the residual frame and the *** results have revealed that our CS-based DVC system yields better rate-distortion performance when compared with other schemes.
WSD can effectively remove random noise of a raw image from very low density to ultra-high den-sity fluorescent molecular distribution scenarios. The size of the raw image that WSD can denoise is subject to the used m...
详细信息
WSD can effectively remove random noise of a raw image from very low density to ultra-high den-sity fluorescent molecular distribution scenarios. The size of the raw image that WSD can denoise is subject to the used measurement matrix. A large raw image must be divided into blocks so that WSD denoises each block separately. Based on traditional single-molecule localization and super-resolution reconstruction scenarios, wide spectrum denoising (WSD) for blocks of different sizes was studied. The denoising ability is related to block sizes. The general trend is when the block gets larger, the denoising effect gets worse. When the block size is equal to 10, the denoising effect is the best. Using compressedsensing, only 20 raw images are needed for reconstruction. The temporal resolution is less than half a second. The spatial resolution is also greatly improved.
Low-complexity coherent detection using self-interference of aggregated optical orthogonal frequency division multiplexing (O-OFDM) subcarriers is proposed. Self-interference among the aggregated O-OFDM subcarriers is...
详细信息
Low-complexity coherent detection using self-interference of aggregated optical orthogonal frequency division multiplexing (O-OFDM) subcarriers is proposed. Self-interference among the aggregated O-OFDM subcarriers is employed to recover their relative phase relationships through the variation in the obtained power spectra. The differences in a few preselected principal spectral components are successfully demonstrated based on the phase states of four O-OFDM subcarriers modulated via quadrature phase shift keying (QPSK). We experimentally verified self-interference and bit error rate reaches 10(-3). The number of bits available in the proposed method increases with the number of subcarriers, gradually approaching that in QPSK beyond OOK.
暂无评论