Image Fusion Algorithm Based on Wavelet Sparse Represented Compressed Sensing

Compressed sensing (CS) leverages signal sparsity in transform domains to facilitate precise signal reconstruction from restricted incoherent measurements. While effectively applied in turbomachinery flow field measurements, current compressed sensing reconstruction research primarily emphasizes random sampling within limited instrumentation parameters, resulting in a significant knowledge deficit regarding high-frequency reconstruction from time-domain uniformly undersampled data. This study addresses this limitation by developing compressed sensing-enhanced temporal resolution for unsteady flow field measurements in compressor cascades. This research presents and implements a dual low-frequency uniform sampling compressive sensing approach for particle image velocimetry analysis in the near-wake areas of compressor blades. The effectiveness of the strategy was validated through comparative analysis with random sampling CS reconstruction. Second, a sensitivity analysis was performed on the principal factors influencing reconstruction accuracy in dual low-frequency sampling CS, including the orthogonal basis, compression ratio, and modal order. The dual low-frequency uniform sampling strategy is ultimately extended to multi-low-frequency sampling, hence confirming the robustness of generalized multi-frequency CS implementations. The findings indicate that the dual low-frequency uniform sampling CS technique markedly decreases the need for instrumentation frequency responsiveness while maintaining measurement reliability. This study develops a methodological framework for high-resolution physical field measurements in turbomachinery applications, providing theoretical foundations and practical implementation guidelines for CS-enhanced experimental fluid dynamics.

Implementation of compressive sensing in ECG and EEG signal processing

Accurate distance information is essential for remote sensing mapping and 3D information reconstruction. Dense depth reconstruction from sparse measurements in indoor and outdoor natural scenes has been extensively researched. However, in aerial scenes, dense height image reconstruction from sparse height measurements has received relatively limited attention. This paper investigates the challenge of reconstructing aerial ground height from sparse height measurements. In this paper, we comprehensively evaluate the feasibility and performance of various sparse reconstruction algorithms in aerial scenes for the first time, and explore the optimal sampling rate and pattern for preserving the image structure and details. Additionally, we propose two novel algorithms based on the normalized weighted non-local Laplacian, which can achieve state-of-the-art results without relying on color image guidance. Moreover, our algorithm is inherently robust to different sampling configurations. The solver tools relied upon also have proven hardware and software optimisation and acceleration schemes in the industry, making them well suited for deployment in real-world scenarios. We validate the effectiveness and robustness of the proposed algorithms on three datasets.

This paper presents modification of the TwIST algorithm for Compressive Sensing MRI images reconstruction. Compressive Sensing is new approach in signal processing whose basic idea is recovering signal form small set of available samples. The application of the Compressive Sensing in biomedical imaging has found great importance. It allows significant lowering of the acquisition time, and therefore, save the patient from the negative impact of the MR apparatus. TwIST is commonly used algorithm for 2D signals reconstruction using Compressive Sensing principle. It is based on the Total Variation minimization. Standard version of the TwIST uses masked 2D Discrete Fourier Transform coefficients as Compressive Sensing measurements. In this paper, different masks and different transformation domains for coefficients selection are tested. Certain percent of the measurements is used from the mask, as well as small number of coefficients outside the mask. Comparative analysis using 2D DFT and 2D DCT coefficients, with different mask shapes is performed. The theory is proved with experimental results.

Wavefields obtained from the measurement of Lamb waves propagating through a solid media by a Laser Doppler Vibrometer (LDV) are very rich in qualitative and quantitative information about structural defects. In this research, Compressed Sens-ing (CS) is used to significantly reduce the number of point measurements necessary to the application of SHM techniques. The process extrapolates the information con-tained in M measurements to reconstruct a wavefield on a grid of P pixels with the condition M < P, using a basis of functions created from the dispersion relations of the media and the propagation laws of lamb waves. Reconstructions of experimental and analytical uni-dimensional wavefields are detailed to validate the concept. The development of this process is a first step towards fast large scale defect detection techniques by LDV in SHM. doi: 10.12783/SHM2015/232

Compressive sensing (CS) is an innovative approach to simultaneously measure and compress signals such as biomedical signals that are sparse or compressible. A major effort in CS is to design a measurement matrix that can be used to encode and compress such signals. The measurement matrix structure has a direct impact on the computational and storage costs as well as the recovered signal quality. Sparse measurement matrices (i.e. with few non-zero elements) may drastically reduce these costs. We propose a permuted Kronecker-based sparse measurement matrix for sensing and data recovery in CS applications. In our study, we use three classes of sub-matrices (normalized Gaussian, Bernoulli, and BCH-based matrices) to create the proposed measurement matrix. Using ECG signals from the MIT-BIH Arrhythmia database, we show that the reconstructed signal quality is comparable to the ones achieved using well known CS methods. Our methodology results in an overall reduction in storage and computations, both during the sensing and recovery process. This approach can be generalized to other classes of eligible measurement matrices in CS.

Thermal Imaging can be really valuable to military, other users of surveillance camera and physicians. Contrary to the usual sampling process where weavers want to sample at the Nyquist rate the Compressive Sensing provides a stricter sampling condition when the signal is known to be sparse or compressible. It turned out that the Nyquist-Shannon theorem is a sufficient condition but not a necessary condition for perfect reconstruction. The compressive sensing field of interest provides a stricter sampling condition when the signal is known to be sparse or compressible. This theorem still struggles with three main problems: sparse representation, measurement matrix and reconstruction algorithm. Unfortunately, thermal image camera resolution is considerably lower than of optical cameras, mostly only 160×120 or 320×240 pixels narrow view. The 360-degree infrared surveillance would be the clear choice. Day or night, the IR Revolution 360 panoramic infrared camera provides instantaneous, long range, wide area, high resolution thermal imaging. The method utilizes double sensor thermal imaging cameras. Moreover the temporal resolution has been enhanced. This paper goal is to keep evolving with compressed sensing and thermal imaging technology.

Electrocardiogram (ECG) is a vital signal which represents the state of health of astronauts in a manned spaceflight mission and hence must be continuously acquired and transmitted throughout the mission. Telemetry bandwidth is a premium resource in such applications. Traditional method of sampling at Nyquist rate is highly bandwidth inefficient. Hence it is advantageous to use Compressive sensing (CS) technique to optimize data at measurement point itself. Conventional CS techniques employ computationally intensive measurement matrices which are not hardware efficient for both acquisition as well as recovery. In this work, a hardware efficient scheme with use of a sparse binary measurement matrix is proposed. The signal is recovered from the compressive measurement using a constraint function based on inverted Laplace distribution function. Gradient decent method is used to recursively recover the original ECG signal from the compressive measurements in an efficient manner. Apart from this, a projection scheme is also proposed to minimize the recovery error. The proposed scheme was extensively evaluated with different ECG samples with different compression ratios. Finally, the proposed scheme was benchmarked with Approximated L0 norm based method and it is found to perform more efficiently in compressively sensing and recovery of ECG signals.

We consider the problem of foreground and background extraction from compressed-sensed (CS) surveillance videos that are captured by a static CS camera. We propose, for the first time in the literature, a principal component analysis (PCA) approach that computes directly in the CS domain the low-rank subspace of the background scene. Rather than computing the conventional L 2-norm-based principal components, which are simply the dominant left singular vectors of the CS-domain data matrix, we compute the principal components under an L 1-norm maximization criterion. The background scene is then obtained by projecting the CS measurement vector onto the L 1 principal components followed by total-variation (TV) minimization image recovery. The proposed L 1-norm procedure directly carries out low-rank background representation without reconstructing the video sequence and, at the same time, exhibits significant robustness against outliers in CS measurements compared to L 2-norm PCA. An adaptive CS- L 1-PCA method is also developed for low-latency video surveillance. Extensive experimental studies described in this paper illustrate and support the theoretical developments.

In deep exploration, we often use high-noise and high-resolution astronomical images because of long distance transmission, cosmic noise interference, or other disturbances. Designing an effective method for high-noise astronomical image denoising plays a crucial role in this field. The famous compressed sensing (CS) has shown to be a successful technique for high-resolution image reconstruction. CS is employed to solve the denoising problem in high-noise astronomical images, and a CS reconstruction model and a CS curvelet soft thresholding (NCCST) reconstruction algorithm are proposed simultaneously. In image denoising, the <italic>l</italic>₁-norm reconstruction model based on CS cannot fully consider the internal structure of the image, thus affecting the reconstruction quality. Combined with the <italic>l</italic>₁-norm reconstruction model and group sparse total variation method, the CS reconstruction model is first established. In this framework, the NCCST algorithm uses an adaptive curvelet adjustment operator proposed to select the sparse coefficients in the stage of image sparsity transform, and then a descending VisuShrink threshold is adopted to pick out these reconstructed astronomical image coefficients in each iteration. The experimental results demonstrate that the algorithm proposed can reconstruct clear images from high-noise and high-resolution astronomical images. Meanwhile, it can preserve more astronomical image details, edges, and textures. Even at a low-compression sampling ratio, this algorithm can achieve superior reconstruction performance. The proposed algorithm can be applied in the satellite receiving station to quickly and accurately reconstruct high-resolution astronomical images with high quality.

Microwave-induced thermal acoustic tomography (MITAT) is an innovative technique to image biomedical tissues based on their electric properties. It has the advantages of both high contrast and high spatial resolution. Image reconstruction method in MITAT is always a critical issue. In this paper, a CS-MITAT (CS: compressive sensing) imaging method is proposed. Compressive sensing (CS) is a recently developed sparse signal representation and analysis framework which handles medical imaging measurements using low sampling rate or increasing imaging quality. The CS-MITAT imaging method applies CS theory to the MITAT for breast tumor imaging. In this method, an over-complete dictionary is established to make sparse measurements in the spatial domain. This treatment greatly saves measurement time. Simulations and experiments with real breast tumor tissues demonstrate the feasibility and effectiveness of the method. Compared with conventional time reversal mirror method which has been used in MITAT research, CS-MITAT provides the same peak signal-to-noise ratio imaging quality by using significantly fewer acoustic sensor positions or scanning times.

A simple but efficient algorithm for multi-focus image fusion is proposed in this paper, which is realized based on Laplacian pyramid decomposition. Firstly, the Laplacian pyramids for each source images are decomposed separately, and then each level of new Laplacian pyramid is fused by adopting a simple fusion rule. Finally, the end fused image is obtained by inverse Laplacian pyramid transform. The experiment showed that this method is effective and can get a fine fusion result for multi-focus images.

Deterministic construction of sparse binary matrices via incremental integer optimization

Time delay estimation (TDE) is a hot research topic in wireless location technology. Compressed sensing (CS) theory has been widely applied to image reconstruction and direction of arrival estimation since it was proposed in 2004. The sparse model can be constructed in time domain for estimating the time delay by using the CS theory. The measurement matrix plays a crucial role in the processing of signal reconstruction which is the core problem of CS theory. Therefore the research in the measurement matrix has becomes a hotspot in recent years. The existing measurement matrix is mainly divided into two categories, i.e., random measurement matrix and deterministic measurement matrix. The performance of random measurement matrix has bottlenecks. Firstly, because of the redundant measurement matrix data, the generation and storage of the random number put forward a high requirement for hardware. Secondly the random matrix can only satisfy the restricted isometry property in a statistical sense. The research of the deterministic measurement matrix is of great value under this background. The parity check matrix of low density parity check (LDPC) code has good performance in CS theory. However, the method of randomly selecting non-zero element position has a certain probability to generate a measurement matrix with a short loop structure during generating LDPC code measurement matrix. The robustness of the reconstruction performance decreases with the increase of iteration times. A novel quasi-cyclic CS algorithm based on progressive edge-growth is constructed to estimate the time delay. The purpose of this article is to deal with the need to store a large number of data in existing measurement matrix during time delay, by using the CS theory. The algorithm presented here can achieve TDE in a high precision. First, the theoretical bridge between CS and the maximum likelihood decoding is established. And the design criterion of measurement matrix based on the LDPC code is derived. The sparse measurement matrix with quasi-cyclic structure is constructed by introducing the idea of progressive edge-growth. Finally, the orthogonal matching pursuit algorithm is used to estimate the time delay. Furthermore, the computational complexity of the algorithm and the data storage of the measurement matrix are analyzed theoretically. Simulations show that the correct reconstruction probability of the proposed approach is higher than those of the Gauss random matrix and random LDPC matrix under the same dimension. Compared with the random LDPC matrix, the proposed method can improve performance at the expense of less complexity under the condition of the same data storage.

Compressed sensing (CS), as a novel theory based on the fact that certain signals can be recovered from a relatively small number of non-adaptive linear projections, is attracting ever-increasing interests in the areas of wireless sensor networks. However, the applications of traditional CS in such settings are limited by the huge transport cost caused by dense measurement. To solve this problem, we propose several ameliorated random routing methods executed with sparse measurement based CS for efficient data gathering corresponding to different networking topologies in typical wireless sensor networking environment, and analyse the relevant performances comparing with those of the existing data gathering schemes, obtaining the conclusion that the proposed schemes are effective in signal reconstruction and efficient in reducing energy consumption cost by routing. Our proposed schemes are also available in heterogeneous networks, for the data to be dealt with in CS are not necessarily homogeneous.