Greedy Pursuit Algorithm Research Articles

SIBS: A sparse encoder utilizing self-inspired bases for efficient image representation

Addressing the limitations of pre-defined dictionaries in image processing, this study introduces Self-Inspired Bases-based Sparse Encoder (SIBS), a novel approach that dynamically generates image-specific atoms by leveraging existing dictionaries and input data. Extensive numerical analysis and simulations demonstrate that SIBS enhances sparse coding performance in three key areas: improved quality resolution via precise image reconstruction, accelerated convergence speed, and competitive compression performance rivaling techniques like JPEG and JP2000. Experiments show that SIBS enhances quality levels and NMSE at the same number of non-zero coefficients and outperforms atoms learned directly from the image at low error levels. SIBS also effectively improves the performance of various learned and structured dictionaries by serving as auxiliary bases, enhancing quality resolution, convergence rate, and dictionary efficiency. Additionally, SIBS has potential as a competitive image compression method. The study’s discussion on SIBS limitations guides future research, including examining its performance with other greedy pursuit algorithms and reevaluating the encoder with other lossless and filter techniques.

The statistical properties analysis of reconstruction error in greedy pursuit algorithms: Taking OMP as an example

AbstractGreedy pursuit algorithms are widely used in sparse signal processing for their computational efficiency. However, research on the reconstruction error properties is far from comprehensive. This paper derives the statistical properties of reconstruction error in greedy pursuit algorithms, including probability density function (PDF), expectation, and covariance. The reconstruction error follows a mixture distribution, which is composed of multiple multivariate random variables and weighted by the probability of support sets. The multivariate random variable obeys a truncated distribution that results from restricting the noise domain. The validity of the derivations is verified by using the orthogonal matching pursuit (OMP) algorithm as an example.

Sound field navigation with virtual higher-order sound sources using complex greedy pursuit algorithm

As the Virtual Reality (VR) and metaverse industries continue to expand rapidly, there is a growing need to capture and recreate real-world experiences in immersive audio-visual scenes. Sound field translation, which activates equivalent virtual sources to recreate spatial sound fields, enables users to navigate through these scenes seamlessly. However, combining recordings from different microphones and processing mixed fields of exterior and interior sources present significant challenges. This paper introduces a novel method for virtual navigation by sparsely decomposing complex sound fields using distributed virtual higher-order sound sources and an iterative complex greedy pursuit algorithm. By combining spatially separated microphone recordings, the technique identifies its sparse representation with several higher-order virtual sources. This process effectively decomposes the complex sound field into a grid of higher-order sources, leveraging the power of the complex greedy pursuit algorithm. Through extensive experimentation, we demonstrate the suitability of our method for applications such as VR navigation and sound field reproduction with binaural devices. The results showcase enhanced realism and accuracy, offering users a truly immersive audio experience in virtual environments. As the demand for realistic audio-visual scenes grows, this innovative approach holds promise for advancing VR technology and enriching user experiences in the metaverse.

Multitarget Enumeration and Localization in Distributed MIMO Radar Based on Energy Modeling and Compressive Sensing

Target localization is one of the most important research topics in the field of radar signal processing. In this paper, the problem of multitarget enumeration and localization in the distributed multiple-input multiple-output (MIMO) radar with noncoherent processing mode is investigated. We first analyze the theoretical bound of the multitarget localization accuracy under the discrete time signal model and the Swerling 1 target model. It is determined by the Cram'r-Rao lower bound (CRLB) at low signal-to-noise ratio (SNR) and the sampling lower bound (SLB) when the SNR is high. Furthermore, an innovative multitarget enumeration and localization scheme is developed, which is based on the energy modeling of the multiple transmitter-receiver paths and the compressive sensing theory. To solve the sparse vector recovery issue, we design a lightweight iterative greedy pursuit algorithm including the similarity evaluation strategy. In addition, an iterative-based target position refinement process is designed to alleviate the off-grid problem caused by the spatial discretization. The proposal utilizes the samples of the raw signals and belongs to the category of the direct localization. Nevertheless, it has significantly higher computational efficiency and lower data communication burden than the conventional direct localization methods, while avoiding the complex data association encountered by the indirect localization methods. Finally, the simulation results validate the effectiveness and robustness of the proposed method.

Multi-scale deep feature fusion based sparse dictionary selection for video summarization

The explosive growth of video data constitutes a series of new challenges in computer vision, and the function of video summarization (VS) is becoming more and more prominent. Recent works have shown the effectiveness of sparse dictionary selection (SDS) based VS, which selects a representative frame set to sufficiently reconstruct a given video. Existing SDS based VS methods use conventional handcrafted features or single-scale deep features, which could diminish their summarization performance due to the underutilization of frame feature representation. Deep learning techniques based on convolutional neural networks (CNNs) exhibit powerful capabilities among various vision tasks, as the CNN provides excellent feature representation. Therefore, in this paper, a multi-scale deep feature fusion based sparse dictionary selection (MSDFF-SDS) is proposed for VS. Specifically, multi-scale features include the directly extracted features from the last fully connected layer and the global average pooling (GAP) processed features from intermediate layers, then VS is formulated as a problem of minimizing the reconstruction error using the multi-scale deep feature fusion. In our formulation, the contribution of each scale of features can be adjusted by a balance parameter, and the row-sparsity consistency of the simultaneous reconstruction coefficient is used to select as few keyframes as possible. The resulting MSDFF-SDS model is solved by using an efficient greedy pursuit algorithm. Experimental results on two benchmark datasets demonstrate that the proposed MSDFF-SDS improves the F-score of keyframe based summarization more than 3% compared with the existing SDS methods, and performs better than most deep-learning methods for skimming based summarization.

Real-Time Data Sensing for Microseismic Monitoring via Adaptive Compressed Sampling

The large amount of monitoring data has posed enormous challenges to the quick response and accurate analysis of microseismic events. Compressed sensing (CS) has the advantages of low resource cost, high efficiency, and excellent data compression ratio, over conventional sensing methods. However, there are still issues to be addressed for its applications: 1) The poor quality and complex signal structure significantly increased the difficulty of keeping satisfactory efficiency; 2) The systematic design of the sparse dictionary, and the measurement matrix for microseismic signal CS are still poor; 3) The conventional recovery algorithms also require prior knowledge of signal sparsity, which is hardly possible to know or estimate in practice. Therefore, an adaptive realtime sensing method for microseismic monitoring from the perspective of systematic design was proposed in this work. We first analyzed noise and signal structure characteristics to construct an over-complete learning dictionary. Secondly, according to the learned dictionary, we analyzed the key performance factors of random projection through comparison between different matrices. Thirdly, we explored the relationship between the signal sparsity and the residual energy decay during data recovery with the greedy pursuit algorithms, and then presented an energy-ratio based sparsity adaptive matching algorithm. Finally, we carried out the performance evaluation of the proposed realtime sensing method through synthetic signals and field monitoring data.

BTGP: Enhancing the perceptual recovery of the image compressive sensing using a backtracking greedy pursuit algorithm

In recent years, compressed sensing has been applied to image representation, and it shows strong ability to represent the image by few bases’ (atoms’) coefficients. This representation is a lossy technique, so, many efforts are applied to enhance the perceptual levels of this type of image modeling by recalculating these coefficients according to an SSIM-based criteria. All these efforts work in the forward direction of the representation, but the atoms’ selection criteria is still MSE-based. So, in this paper, we propose a backward enhancement technique whose selection criteria is an SSIM-based. Comprehensive numerical simulations have been conducted on different datasets like CVG-UGR, USC-SIPI, Linnaeus 5, where the results are compared with several algorithms. The results obtained by these simulations have proved that the proposed method is capable of enhancing the perceptual quality levels of the forward greedy pursuit stage by selecting the atoms which have good perceptual effect, and removing the unnecessary atoms which may distort the image perceptually rather than enhancing it.

Absolute Distance Measurement Based on Self-Mixing Interferometry Using Compressed Sensing

An absolute distance measurement sensor based on self-mixing interferometry (SMI) is suitable for application in aerospace due to its small size and light weight. However, an SMI signal with a high sampling rate places a burden on sampling devices and other onboard sources. SMI distance measurement using compressed sensing (CS) is proposed in this work to relieve this burden. The SMI signal was sampled via a measurement matrix at a sampling rate lower than Nyquist’s law and then recovered by the greedy pursuit algorithm. The recovery algorithm was improved to increase its robustness and iteration speed. On a distance measuring system with a measurement error of 60 µm, the difference between raw data with 1800 points and CS recovered data with 300 points was within 0.15 µm, demonstrating the feasibility of SMI distance measurement using CS.

Bayesian Inference-Aided Channel Estimation for Hybrid Full-Dimensional MIMO Systems

Efficient channel estimation is challenging in full-dimensional multiple-input multiple-output communication systems, particularly in those with hybrid digital-analog architectures. Under a compressive sensing framework, this letter first designs a uniform dictionary based on a spherical Fibonacci grid to represent channels in a sparse domain, yielding smaller angular errors in three-dimensional beamspace than traditional dictionaries and consistent estimation in different directions. Then, a Bayesian inference-aided greedy pursuit algorithm is developed to estimate channels in the frequency domain. Finally, simulation results demonstrate that both the designed dictionary and the proposed Bayesian inference-aided channel estimation outperform the benchmark schemes and attain a lower normalized mean squared error of channel estimation.

A new greedy sparse recovery algorithm for fast solving sparse representation

Kernel sparse representation-based classification (KSRC) in compressive sensing represents one of the most interesting research areas in pattern recognition and image processing. Nevertheless, KSRC is subjected to some shortcomings. KSRC is greedy in time to achieve an approximate solution of sparse representation based on $$\ell_{1}$$ -norm minimization. A diversity of greedy recovery algorithms have been tested in order to decrease computational complexity compared to the optimal $$\ell_{1}$$ -norm minimization while keeping a proved reconstruction accuracy. In this research, we suggest a new greedy recovery algorithm, called the fast reduced sampling matching pursuit (FRSMP). Unlike previous greedy recovery algorithms which applied too many or very few values per iteration, FRSMP selects a sufficient number of elements. Moreover, FRSMP performs the least square minimization iteratively through the Sherman–Morrison–Woodbury formula, to avoid large matrix inversion which results in a significant speedup. Experimental results with both noisy and noiseless data have shown that the proposed FRSMP method achieves a higher reconstruction accuracy at low reconstruction time compared to other greedy pursuit algorithms. Also, experiments on frequent face databases have proven that the KSRC-based FRSMP method shows reliable and higher recognition rate and computation time compared with other advanced sparse representation methods for face recognition.

Learned Greedy Method (LGM): A novel neural architecture for sparse coding and beyond

The fields of signal and image processing have been deeply influenced by the introduction of deep neural networks. Despite their impressive success, the architectures used in these solutions come with no clear justification, being “black box” machines that lack interpretability. A constructive remedy to this drawback is a systematic design of networks by unfolding well-understood iterative algorithms. A popular representative of this approach is LISTA, evaluating sparse representations of processed signals. In this paper, we revisit this task and propose an unfolded version of a greedy pursuit algorithm for the same goal. More specifically, we concentrate on the well-known OMP algorithm, and introduce its unfolded and learned version. Key features of our Learned Greedy Method (LGM) are the ability to accommodate a dynamic number of unfolded layers, and a stopping mechanism based on representation error. We develop several variants of the proposed LGM architecture and demonstrate their flexibility and efficiency.

ANN-Assisted CoSaMP Algorithm for Linear Electromagnetic Imaging of Spatially Sparse Domains

Greedy pursuit algorithms (GPAs) are widely used to reconstruct sparse signals. Even though many electromagnetic (EM) inverse scattering problems are solved on sparse investigation domains, GPAs have rarely been used for this purpose. This is because (i) they require a priori knowledge of the sparsity level in the investigation domain, which is often not available in EM imaging applications, and (ii) the EM scattering matrix does not satisfy the restricted isometric property. In this work, these challenges are respectively addressed by (i) using an artificial neural network (ANN) to estimate the sparsity level, and (ii) adding a Tikhonov regularization term to the diagonal elements of the scattering matrix. These enhancements permit the compressive sampling matching pursuit (CoSaMP) algorithm to be efficiently used to solve the two-dimensional EM inverse scattering problem, which is linearized using the Born approximation, on spatially sparse investigation domains. Numerical results, which demonstrate the efficiency and applicability of the proposed ANN-enhanced CoSaMP algorithm, are provided.

Constrained Backtracking Matching Pursuit Algorithm for Image Reconstruction in Compressed Sensing

Image reconstruction based on sparse constraints is an important research topic in compressed sensing. Sparsity adaptive matching pursuit (SAMP) is a greedy pursuit reconstruction algorithm, which reconstructs signals without prior information of the sparsity level and potentially presents better reconstruction performance than other greedy pursuit algorithms. However, SAMP still suffers from being sensitive to the step size selection at high sub-sampling ratios. To solve this problem, this paper proposes a constrained backtracking matching pursuit (CBMP) algorithm for image reconstruction. The composite strategy, including two kinds of constraints, effectively controls the increment of the estimated sparsity level at different stages and accurately estimates the true support set of images. Based on the relationship analysis between the signal and measurement, an energy criterion is also proposed as a constraint. At the same time, the four-to-one rule is improved as an extra constraint. Comprehensive experimental results demonstrate that the proposed CBMP yields better performance and further stability than other greedy pursuit algorithms for image reconstruction.

Atom selection strategy for signal compressed recovery based on sensing information entropy

In greedy pursuit algorithm, atom selection is commonly a concerned topic for signal compressed recovery. To improve the recovery performance, an optimal atom selection strategy without the prior information is proposed in this paper. The sensing information entropy is defined to prune the possible false atoms in the estimated support set. Fewer iterations are required in the proposed strategy and it can also be applied in the case with high sparsity level or low signal-noise-ratio. Compared with the existing representative algorithms, the superiority of the recovery error and probability is verified by the simulations. Furthermore, the proposed method is applied to recover the real random modulated signal. The results show that the recovered signal has greater consistence with the original input signal.

Design and Application of a Greedy Pursuit Algorithm Adapted to Overcomplete Dictionary for Sparse Signal Recovery

Compressive sensing (CS) is a novel paradigm to recover a sparse signal in compressed domain. In some overcomplete dictionaries, most practical signals are sparse rather than orthonormal. Signal space greedy method can derive the optimal or near-optimal projections, making it possible to identify a few most relevant dictionary atoms of an arbitrary signal. More practically, such projections can be processed by standard CS recovery algorithms. This paper proposes a signal space subspace pursuit (SSSP) method to compute spare signal representations with overcomplete dictionaries, whenever the sensing matrix satisfies the restricted isometry property adapted to dictionary (D-RIP). Specifically, theoretical guarantees were provided to recover the signals from their measurements with overwhelming probability, as long as the sensing matrix satisfies the D-RIP. In addition, a thorough analysis was performed to minimize the number of measurements required for such guarantees. Simulation results demonstrate the validity of our hypothetical theory, as well as the superiority of the proposed approach.

Low-Complexity Subspace-Aided Compressive Spectrum Sensing Over Wideband Whitespace

Compressive sensing (CS) techniques have been proposed for wideband spectrum sensing applications to achieve sub-Nyquist-rate sampling. The complexity of CS recovery algorithm and the detection performance against noise are two of the main challenges of the implementation of compressive spectrum sensing (CSS). Greedy algorithms have been of particular interest in CSS due to low complexity. We firstly propose a novel spectrum sparsity estimation scheme directly from sub-Nyquist measurements, with which the computational effort of greedy pursuit algorithms can be saved and recovery performance improved. Besides, the spectrum sparsity estimates also enable hard detection of channel occupancy where threshold adaption for energy detection is avoided. Moreover, with the detected dimension of signal subspace, we propose to implement joint-block-sparse multiple-measurement-vector (MMV) model of CSS whose dimension can be reduced to minimum and meanwhile a large portion of noise is removed. The proposed MMV model with noise and dimension reduction further improves the detection performance and also keeps the complexity low. Finally, we generalize the hard thresholding pursuit (HTP) algorithm to recover joint-block-sparse signals. In simulations, the detection performance and complexity of the proposed CSS scheme show striking superiority against multiple benchmarking schemes.

Sparse signal reconstruction via expanded subspace pursuit

Due to their low computational complexity, greedy pursuit algorithms are widely used in sparse signal reconstruction. An improved greedy iterative algorithm, called the expanded subspace pursuit, is proposed. By incorporating a simple backtracking technique, the proposed algorithm removes the mismatching atoms to refine the estimated support set effectively. Furthermore, the proposed algorithm can achieve blind sparse reconstruction even without the prior of the sparsity degree. Compared with other greedy algorithms, the proposed algorithm exhibits superior reconstruction accuracy and lower computational complexity. Finally, numerical results are presented to demonstrate the validity of the proposed algorithm.

Stage-Determined Matching Pursuit for Sparse Channel Estimation in OFDM Systems

As a sampling paradigm to recover the sparse or compressible signals from very few incoherent linear measurements, compressed sensing (CS) has spurred much interest in recent years. Since tractable recovery algorithm is a crucial and major issue of CS, the greedy pursuit (GP) algorithms are generally preferred to enable accurate reconstruction of sparse or compressible signals from very few noisy incoherent measurements. While selecting multiple “correct” indices per iteration to improve the running time of orthogonal matching pursuit algorithm, the chosen indices are usually not the optimal one due to the iterative short-sighted decisions. In this paper, since the demand for fast reconstruction algorithms-possibly operating in linear time-is of significant interest, an algorithm namely, stage-determined matching pursuit (SdMP) is proposed. The SdMP algorithm exploits the selection of few indices (below the target signal sparsity level) per iteration, and then combines a backtracking or pruning step in some later iterations-albeit after satisfying a sparsity level conditions to refine the selected set. Using the restricted isometry property, the theoretical analysis of the SdMP algorithm and the sufficient conditions (guarantees) for realizing an improved reconstruction performance are presented. Through numerical simulations, it is shown that SdMP outperforms many GP algorithms that select multiple indices per iteration in terms of reconstruction accuracy and the running speed.

Joint-Sparse Signal Reconstruction Based on Common Support Set Refinement

Joint-sparse signal reconstruction is a key issue in distributed compressed sensing based on the mixed support set model. In this letter, a novel joint-sparse signal reconstruction algorithm is proposed based on the common support set refinement. The common support set is first roughly estimated by greedy pursuit algorithms. The roughly estimated common support set is then refined by pruning the incorrect elements. With the refined common support set, greedy pursuit is utilized to reconstruct the joint-sparse signals. The complexity analysis and simulation results indicate that the proposed algorithm achieves better estimates of the support sets and finally reduces the reconstruction error for the joint-sparse signals with a moderate complexity compared with the state-of-the-art algorithms.

Improving the Signal-to-Noise Ratio of Superresolution Imaging Based on Single-Pixel Camera

Based on the theories of single-pixel camera and compressed sensing image reconstruction, the sparse basis, the projection method of measurement matrix, and the signal reconstruction algorithm are optimized. First, for the sparse representation of image, the restraint matrix is designed combining the characteristics of wavelet sparse coefficients to enhance the sparse representation ability of the discrete wavelet base, which improves the quality of image reconstruction and imaging by single-pixel camera. Then, in the single-pixel camera system, the projection method is improved according to the characteristics of the digital mirror device micromirror, and a new bilateral projection method based on the block diagonal measurement matrix is proposed to realize the superresolution imaging of the outdoor scene, reducing the number of measurement and improving the imaging quality. Finally, for the algorithm of image reconstruction, combining the characteristics of convex optimization and nonconvex optimization algorithms, a new algorithm from convex optimization approximately to nonconvex optimization algorithm is proposed, and compared with the traditional image reconstruction algorithm, such as greedy pursuit algorithm, minimum norm algorithm, and image interpolation, the peak signal-to-noise ratio and imaging quality of reconstructed images are effectively improved. The feasibility of the proposed methods is demonstrated by simulation experiments and imaging experiments of single-pixel camera.