Regularized Orthogonal Matching Pursuit Research Articles

Method for Brillouin gain spectrum recovery based on compressed sensing with convex optimization

The traditional Brillouin optical fiber distributed sensors obtain the Brillouin gain spectrum (BGS) through frequency-by-frequency sweeping acquisition, which can be time-consuming and data intensive. These characteristics put a lot of pressure on data storage, especially on signal processing. Compressed sensing is a method represented by random sampling to reduce the number of acquisition frequencies, but the results obtained may be unstable. In this paper, we have proposed a reconstruction algorithm based on compressed sensing with convex optimization (COP), which can recover the whole BGS by collecting only 10% of the acquisition frequencies. The recovered BGS can attain a RMSE similar to the fully collected BGS. The proposed algorithm also provides more accurate and stable performances for different random sampling points compared to existing reconstruction methods. For example, for a 10% sampling percentage, with a reduction in error of 2.24 and 0.40 MHz, values are lower than those employing the orthogonal matching pursuit (OMP) and the regularized orthogonal matching pursuit (ROMP), respectively. Moreover, the reconstruction results of the proposed method are more stable for different random sampling points, with a reduction in standard deviation of 2.58 and 0.07 MHz.

A Novel Meta-Analysis-Based Regularized Orthogonal Matching Pursuit Algorithm to Predict Lung Cancer with Selected Biomarkers

Biomarker selection for predictive analytics encounters the problem of identifying a minimal-size subset of genes that is maximally predictive of an outcome of interest. For lung cancer gene expression datasets, it is a great challenge to handle the characteristics of small sample size, high dimensionality, high noise as well as the low reproducibility of important biomarkers in different studies. In this paper, our proposed meta-analysis-based regularized orthogonal matching pursuit (MA-ROMP) algorithm not only gains strength by using multiple datasets to identify important genomic biomarkers efficiently, but also keeps the selection flexible among datasets to take into account data heterogeneity through a hierarchical decomposition on regression coefficients. For a case study of lung cancer, we downloaded GSE10072, GSE19188 and GSE19804 from the GEO database with inconsistent experimental conditions, sample preparation methods, different study groups, etc. Compared with state-of-the-art methods, our method shows the highest accuracy, of up to 95.63%, with the best discriminative ability (AUC 0.9756) as well as a more than 15-fold decrease in its training time. The experimental results on both simulated data and several lung cancer gene expression datasets demonstrate that MA-ROMP is a more effective tool for biomarker selection and learning cancer prediction.

A novel block compressive sensing algorithm for SAR image formation

Compressive Sensing (CS) theory has been used for Synthetic Aperture Radar (SAR) imaging due to the sparsity feature of SAR images. Therefore, some well-known CS algorithms like Orthogonal Matching Pursuit (OMP) and Regularized OMP (ROMP) methods have been employed for SAR image formation with a very small number of samples. On the other hand, it has been shown that the SAR signal is consistent with the definition of block sparsity. Hence, compressive sensing methods employing block structure, known as Block Compressive Sensing (BCS), are presented and used for SAR image formation to achieve more accuracy with a smaller number of samples. In this paper, first, a new BCS-based algorithm, namely, Block Norm Regularized Orthogonal Matching Pursuit (BNROMP), is introduced which can be used in all BCS applications. Then, this novel method is used for SAR image formation to achieve more accuracy and excellent resolution with a small number of samples. The simulation results for the synthesized data, as well as real data, show that by using the novel BNROMP method, we could form SAR images with higher quality, as compared to those for the standard image formation algorithms and other CS-SAR or BCS-SAR methods.

A Novel Regularized Adaptive Matching Pursuit for Moving Force Identification Using Multiple Criteria and Prior Knowledge

Moving force identification (MFI) is one of the challenging tasks in structural health monitoring (SHM) of bridges. As an inverse problem, continuous attention is needed to address the ill-posedness of MFI system matrix, computational efficiency and accuracy. Therefore, a novel regularized adaptive matching pursuit (NRAMP) framework is proposed for MFI using multiple criteria and prior knowledge in this study. Firstly, a relationship between moving forces and structural responses is established. With the utilization of redundant matrix, the MFI problem is converted into one of the sparse recoveries. A new adaptive criterion related to atoms both in the sparse regularization and LSQR factorization is introduced into the regularized orthogonal matching pursuit (ROMP) process. The ill-posedness of system matrix in sparse recovery can be reduced greatly, and the unknown sparsity problem can be skipped. Furthermore, the optimal atoms of redundant matrix will be selected repeatedly based on another criterion related to prior knowledge that the static axle-weight of a vehicle is the main component of moving vehicle force. The residual in each iteration will be saved and the atoms with the smallest residual are chosen at last. Finally, to assess the feasibility of the proposed method, numerical simulations on identification of single moving force with impulse components and two unequal moving forces, and experimental verifications on MFI of a model vehicle moving on a beam in laboratory are also carried out. The results show that the relative percentage errors between the identified and true gross vehicle weight keep under 3.6% in all measured cases, and the executive time of the proposed method is far less than that due to common OMP methods.

Performance analysis of beamforming algorithm based on compressed sensing

The beamforming (BF) algorithm is widely used in sound source recognition due to its superior performance, but its main lobe is wide, side lobes are high, and its running speed is slow. Therefore, a method based on the compressed sensing beamforming method is proposed. The sound source measurement model is established, the compressed sensing reconstruction matrix is applied to the beamforming method, and propose a compressed sensing beamforming sound source recognition method. The sound source recognition performance of orthogonal matching pursuit (OMP), generalized orthogonal matching pursuit (gOMP), and regularized orthogonal matching pursuit (ROMP) is compared and analyzed through MATLAB simulation, and the OMP algorithm is selected to combine with the beamforming method. Further study the OMP-BF way and compare and analyze the recognition accuracy and running time of OMP-BF with functional beamforming (F-BF) and L1 minimum norm method beamforming (L1-BF). The results show that the OMP-BF method can accurately identify the sound source location, and the running time is much lower than L1-BF and F-BF. Finally, through experiments, the effectiveness of the algorithm is verified.

Compressed Sensing Based on K-SVD for Brillouin Optical Fiber Distributed Sensors

The continuous operation of Brillouin optical fiber distributed sensors requires the acquisition and processing of large amount of data that imposes ample pressure on the data acquisition systems and storage devices. To overcome such limitations, the compressed sensing (CS) method based on K-Singular value decomposition (K-SVD) algorithm as transform is proposed in this paper for the accurate extraction of sensing information with less data acquired from Brillouin optical fiber distributed sensors without the hardware modification. In such algorithm, the parameters of the K-SVD dictionary are selected first through simulation and the signals are sampled and reconstructed successfully. Then, we apply the regularized orthogonal matching pursuit (ROMP) reconstruction algorithm to effectively reconstruct the experimental data obtained with different sampling rates, frequency steps and test temperatures. We also compare the performances of the CS method based on K-SVD with that based on discrete cosine transform (DCT), discrete Fourier transform (DFT) and principle component analysis (PCA) as transforms. The experimental results show that the proposed method can effectively reconstruct the experimental signals with much reduced amount of data as compared to other methods. The proposed method also provides satisfactory measurement accuracy in extracting sensing information. Therefore, the K-SVD based CS method can be an attractive alternative to make Brillouin optical fiber distributed sensors more suitable for faster operation.

Spatial Shift Phenomenon Compensation for TomoSAR Imaging Using High-Resolution TerraSAR-X Data

Massive high-resolution spaceborne synthetic aperture radar (SAR) data are available nowadays, effecting rapid development in the urban remote sensing technology. In this study, we use a set of 27 scenes from TerraSAR-X to reconstruct the three-dimensional (3D) point clouds of a skyscraper-North Star Times Tower in Beijing, China. We study in detail the derivation process of a 3D model of tomographic SAR (TomoSAR) from the two-dimensional (2D) imaging mathematical model of SAR. We observe the presence of a spatial shift in the elevation direction of TomoSAR, which yields poor and even incorrect results when greedy algorithms such as orthogonal matching pursuit (OMP) or regularized orthogonal matching pursuit (ROMP) algorithms are applied. Then, we propose a phase compensation method to eliminate the spatial shift. Both OMP and ROMP algorithms are used for TomoSAR imaging on high-resolution TerraSAR-X data. The experimental results with North Star Times Tower demonstrate the accuracy of the theoretical analysis and the effectiveness of the algorithms. Finally, we compare the ROMP and OMP algorithms and conclude that both algorithms can yield similar reconstruction results in TomoSAR imaging. The ROMP algorithm does not depend on sparsity and can suppress noise through regularization selection at the cost of time. The OMP algorithm introduces noise when the sparsity is inaccurate.

Millimeter Wave Massive MIMO Channel Estimation Using Subspace Pursuit Greedy Algorithm

Achieving high data rate communications and increasing system reliability are the essentials for 5G networks. Massive MIMO and millimeter wave (mmWave) communications along with the ongoing developments in the underlying infrastructure promise to sharply increase the aggregate capacity. The communication system harnessing the odds of the unused spectrum in mmWave bands is vulnerable to the extreme path loss that severely weakens the strength of the information-bearing signal. Nevertheless, exploiting hybrid beamforming and efficient high-speed channel estimation algorithm can help address this problem and create the communication systems required for 5G. Our main contribution in this paper is to propose a very high speed accurate greedy algorithm called Subspace Pursuit (SP) and we also compare the performance of this algorithm with two other greedy algorithms. Simulation results show that SP algorithm achieves a noticeable improvement in comparison with Orthogonal Matching Pursuit (OMP) and Regularized Orthogonal Matching Pursuit (ROMP) algorithms in terms of both the spectral efficiency and runtime.

Cancellation of Matched Filter Sidelobes for LFM Radar using Regularized Orthogonal Matching Pursuit

Major disadvantage of matched filter is with sidelobes as they might cause false alarms or may mask weak targets of radar echo. In applications like Urban sensing, Through the wall radar, Non destructive testing etc small objects of interest play crucial role which might be masked by sidelobes of matched filter or sometimes sidelobes may be mistreated as objects of interest that lead to false alarms. Many solutions have been proposed in the literature to suppress these sidelobe levels to some extent but not completely cancelled. In this paper, a new approach is utilized to completely cancel the sidelobes of matched filter using a greedy algorithm known as Regularized Orthogonal Matching Pursuit (ROMP). This algorithm is applied to the matched filter output that resulted in complete removal of sidelobes. Also SNR is improved. Even at very low SNRs targets are detected with high probability and hence the proposed approach is more robust to noise.

Sparse recovery based compressive sensing algorithms for diffuse optical tomography

The optical parameters of a tissue such as a highly turbid medium can be reconstructed by the diffuse optical tomography. It is well known that the inverse problem of DOT is nonlinear, unstable and ill posed due to the propagation of photons through the tissue in a zig-zag manner. Though conventional iterative methods have been employed to solve this problem, they seem to be unsuccessful, considering the complex geometries for study. Recently, the compressive sensing (CS) technique has emerged as recent trend in DOT because of its sparse reconstructions for biomedical applications. The main goal of this paper is to formulate the inverse problem as a single measurement vector (SMV) problem by employing the given CS framework. The greedy algorithms such as compressive sampling matching pursuit (CoSaMP), regularized orthogonal matching pursuit (ROMP), stagewise orthogonal matching pursuit (StOMP), and orthogonal matching pursuit (OMP) are extensively studied to reconstruct the 2D map of the absorption parameter change from the tissue boundary data. The conventional method such as least square technique is studied for comparison. The experimental validation of the greedy algorithms is done on a wax circular phantom through a DOT experimental setup. The performance metrics such as mean square error (MSE), structural similarity index (SSIM), and normalized mean square error (NMSE), are used to assess the performance of the DOT imaging in this paper. The extensive study of the simulation results confirm that the greedy algorithms specially, CoSaMP outperform the conventional methods in DOT.

A Matching Pursuit Algorithm for Backtracking Regularization Based on Energy Sorting

The signal reconstruction quality has become a critical factor in compressed sensing at present. This paper proposes a matching pursuit algorithm for backtracking regularization based on energy sorting. This algorithm uses energy sorting for secondary atom screening to delete individual wrong atoms through the regularized orthogonal matching pursuit (ROMP) algorithm backtracking. The support set is continuously updated and expanded during each iteration. While the signal energy distribution is not uniform, or the energy distribution is in an extreme state, the reconstructive performance of the ROMP algorithm becomes unstable if the maximum energy is still taken as the selection criterion. The proposed method for the regularized orthogonal matching pursuit algorithm can be adopted to improve those drawbacks in signal reconstruction due to its high reconstruction efficiency. The experimental results show that the algorithm has a proper reconstruction.

Sparsity-Aware Nonlinear Equalization With Greedy Algorithms for LED-Based Visible Light Communication Systems

The nonlinearity of light emitting diode (LED) in visible light communication (VLC) systems is considered as one major limiting factor that deteriorates the systems’ performance. In this paper, the nonlinear equalization in VLC systems is deemed to be a sparse recovery problem. Three different greedy sparse recovery algorithms, namely matching pursuit (MP), orthogonal MP (OMP), and regularized OMP (ROMP) are employed in constructing the sparsity-aware nonlinear equalizer for LED-based VLC systems. By adopting these greedy algorithms, the number of kernels in the nonlinear equalizer can be significantly reduced with minor performance loss, which enables low-complexity and high-performance nonlinear equalization. The performance of the proposed sparsity-aware nonlinear equalizers is investigated experimentally in orthogonal frequency division multiplexing (OFDM) based VLC systems with commercially available red-green-blue LEDs. The results show that, with the help of greedy sparse recovery algorithms, the number of kernels in nonlinear equalization can be reduced by 32.5%∼62.5% for only 0.5-dB signal-to-noise ratio loss. The compatibility of the proposed sparsity-aware nonlinear equalizer in a ∼1 Gbit/s adaptive bit-power loading OFDM VLC system is also experimentally demonstrated. The ROMP-based nonlinear equalizer is found to be the best choice that offers the optimal balance between performance and complexity, which achieves almost the same performance as the conventional Volterra time domain nonlinear equalizer in OFDM VLC systems with approximately halved number of kernels.

Reconstruction of missing seismic traces based on sparse dictionary learning and the optimization of measurement matrices

Due to limitations arising under complicated geological conditions and field collection environments, we often cannot collect complete and regular field seismic data. To solve that problem, the reconstruction of seismic data has been widely studied. In this paper, we propose a reconstruction algorithm for seismic data with missing traces based on sparse dictionary learning and measurement matrix optimization. The algorithm views the seismic data as a matrix. It first uses the neighboring channel to fill in the missing trace and then uses the transposed matrix and applies the K-singular value decomposition (K-SVD) algorithm by columns to train the sample, obtaining an over-complete dictionary that can be used to develop an optimal sparse representation of seismic data. In the process of seismic data reconstruction, we first transpose the seismic data with missing traces, adopt the regularized orthogonal matching pursuit (ROMP) algorithm to obtain optimum estimations of the data in each column and then transpose the matrix to obtain the reconstructed seismic data. To further increase the quality of seismic data reconstructions, the algorithm presented in this paper also introduces the Equiangular Tight Frame (ETF) method to optimize the measurement matrix. The experiments indicate that this paper's algorithm can achieve high-quality reconstructions of seismic data.

Compressive Sensing-Based Channel Estimation for FBMC-OQAM System Under Doubly Selective Channels

Filter-bank multicarrier with offset quadrature amplitude modulation (FBMC-OQAM) has been considered as an alternative scheme to orthogonal frequency division multiplexing (OFDM). However, the traditional channel estimation techniques of the OFDM cannot be directly applied to the FBMC-OQAM system because of the real-field orthogonality of the FBMC-OQAM signals. Although traditional channel estimation techniques, such as least square (LS) and minimum mean square error (MMSE), are widely applied to the FBMC-OQAM system via canceling the intrinsic imaginary interference from adjacent data symbols, the LS algorithm is subject to noise enhancement and it results in large mean square error (MSE), while the mmse algorithm needs to know the statistical information of channel in advance. Due to sparsity of the wireless channel, channel estimation is investigated as a compressive sensing (CS) problem. In this paper, we first introduce the coding method to cancel intrinsic imaginary interference for the FBMC-OQAM system. Then, a novel sparse adaptive subspace pursuit (SASP) method is proposed to improve the accuracy of LS channel estimation. Finally, we develop two distinctive algorithms, namely, auxiliary pilot (AP) SASP and coding-SASP, to estimate channel frequency respond (CFR) in the FBMC-OQAM system. The simulation results show that the AP-SASP and coding-SASP algorithms can offer a low complexity and fewer measurements compared with conventional orthogonal matching pursuit (OMP) and regularized OMP (ROMP) methods. Moreover, the proposed AP-SASP and coding-SASP algorithms have a better bit error ratio (BER) performance than the conventional OMP and ROMP methods for FBMC system in the doubly selective channels.

Greedy algorithms for diffuse optical tomography reconstruction

Diffuse optical tomography (DOT) is a noninvasive imaging modality that reconstructs the optical parameters of a highly scattering medium. However, the inverse problem of DOT is ill-posed and highly nonlinear due to the zig-zag propagation of photons that diffuses through the cross section of tissue. The conventional DOT imaging methods iteratively compute the solution of forward diffusion equation solver which makes the problem computationally expensive. Also, these methods fail when the geometry is complex. Recently, the theory of compressive sensing (CS) has received considerable attention because of its efficient use in biomedical imaging applications. The objective of this paper is to solve a given DOT inverse problem by using compressive sensing framework and various Greedy algorithms such as orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP), and stagewise orthogonal matching pursuit (StOMP), regularized orthogonal matching pursuit (ROMP) and simultaneous orthogonal matching pursuit (S-OMP) have been studied to reconstruct the change in the absorption parameter i.e, Δα from the boundary data. Also, the Greedy algorithms have been validated experimentally on a paraffin wax rectangular phantom through a well designed experimental set up. We also have studied the conventional DOT methods like least square method and truncated singular value decomposition (TSVD) for comparison. One of the main features of this work is the usage of less number of source–detector pairs, which can facilitate the use of DOT in routine applications of screening. The performance metrics such as mean square error (MSE), normalized mean square error (NMSE), structural similarity index (SSIM), and peak signal to noise ratio (PSNR) have been used to evaluate the performance of the algorithms mentioned in this paper. Extensive simulation results confirm that CS based DOT reconstruction outperforms the conventional DOT imaging methods in terms of computational efficiency. The main advantage of this study is that the forward diffusion equation solver need not be repeatedly solved.

An improved reconstruction algorithm based on compressed sensing for power quality analysis

AbstractThe application and analysis of compressive sensing theory in power quality has been received more and more attention. Reconstruction algorithm is one of the most important contents of the compressive sensing theory, and as one of the reconstruction algorithms with its excellent reconstruction performance, the regularized Orthogonal Matching Pursuit algorithm is widely used. Based on the analysis of the Regularized Orthogonal Matching Pursuit (ROMP) algorithm, an improved Dice-Regularized Orthogonal Matching Pursuit algorithm is proposed. Use the idea of normalization to change the selection rule of element groups and use the Dice coefficient to calculate the similarity between elements and residuals, which can effectively improve the reconstruction performance of the algorithm. Simulation results show that the improved algorithm has better performance than the ROMP algorithm in each index, and the validity and reliability is proved.

Accelerating Doppler Ultrasound Image Reconstruction via Parallel Compressed Sensing

Background: Doppler ultrasound is an important diagnostic tools used to view blood flow through the vessels. For the reconstruction we need to collect a large data to get a Doppler image with high performance. Objective: In this work, we propose an algorithm that combines compressed sensing (CS) and parallel computing to reconstruct the Doppler ultrasound signal and reduce the reconstruction time. Methods: Compressed sensing is a new sampling methods, appeared a few years ago, but it was used in different practical applications such as speeding up MRI scans by acquiring less data to achieve a given amount of resolution and Doppler ultrasound signal reconstruction using fewer measurements to achieve an image with high quality. The main idea of parallel signal/image reconstruction is to divide the main tasks into subtasks and solve them concurrently, in such way that total time can be divided between total tasks. Results: The reconstruction performed using Matlab on a personal computer running a Windows 7 operating system. Real and simulated Doppler data were used for the proposed algorithm validation. The result shows that as the number of cores increased the process time decreased. The image quality from serial programming is same as that a achieved by using parallel programming. The best quality of the image gain is when the 1-norm algorithm used. The lowest reconstruction time was obtained by combining the regularized orthogonal matching pursuit (ROMP) algorithm and parallel computing, with a reconstruction time less than 0.016 seconds when four cores were used and less than 0.034 seconds when two cores were used for 5% of the data. When 80% of the data used the reconstruction time for two cores was 0.109 and for four cores the time was 0.067. The best efficiency was achieved by parallelizing ROMP in two and four cores and the lowest efficiency achieved by parallelized CoSaMP algorithm. The excitation cost decreased with decreasing the numbers of cores. In all the reconstruction algorithms used to perform this work, four cores gave a lower excitation cost than those obtained with two cores. The lowest excitation cost was achieved via ROMP when four cores and fewer measurements were used (0.06) and higher cost gained by using 1-norm algorithm (12.42). The ROMP combined algorithm gives best result among all combined reconstruction algorithm used. Conclusion: We have demonstrated that it is possible to combine compressed sensing and parallel computing to reconstruct the Doppler ultrasound signal. The result of reconstructing the Doppler signal shows that combined algorithm leads to a reduction in reconstruction time and gives an image in realtime while reducing the computation complexity without affecting the image quality. Keywords: Doppler ultrasound signal, compressed sensing, multi-core processor, parallel computing, reconstruction, parfor.

Effective and robust approach for fluorescence molecular tomography based on CoSaMP and SP3 model

Fluorescence molecular tomography (FMT) allows the detection and quantification of various biological processes in small animals in vivo, which expands the horizons of pre-clinical research and drug development. Efficient three-dimensional (3D) reconstruction algorithm is the key to accurate localization and quantification of fluorescent target in FMT. In this paper, 3D reconstruction of FMT is regarded as a sparse signal recovery problem and the compressive sampling matching pursuit (CoSaMP) algorithm is adopted to obtain greedy recovery of fluorescent signals. Moreover, to reduce the modeling error, the simplified spherical harmonics approximation to the radiative transfer equation (RTE), more specifically [Formula: see text], is utilized to describe light propagation in biological tissues. The performance of the proposed reconstruction method is thoroughly evaluated by simulations on a 3D digital mouse model by comparing it with three representative greedy methods including orthogonal matching pursuit (OMP), stagewise OMP(StOMP), and regularized OMP (ROMP). The CoSaMP combined with [Formula: see text] shows an improvement in reconstruction accuracy and exhibits distinct advantages over the comparative algorithms in multiple targets resolving. Stability analysis suggests that CoSaMP is robust to noise and performs stably with reduction of measurements. The feasibility and reconstruction accuracy of the proposed method are further validated by phantom experimental data.

Medical Image Denoising based on Log-Gabor Wavelet Dictionary and K-SVD Algorithm

Medical image denoising is the main step in medical diagnosis, which removes the noise without affecting relevant features of the image. There are many algorithms that can be used to reduce the noise such as: threshold and the sparse representation. The K-SVD is one of the most popular sparse representation algorithms, which is depend on Orthogonal Matching Pursuit (OMP) and Discrete Cosine Transform (DCT) dictionary. In this paper, an algorithm for image denoising was designed to develop K-SVD by using Regularized Orthogonal Matching Pursuit (ROMP) over log Gabor wavelet adaptive dictionary. To evaluate the performance of the proposed techniques, the results were compared with the results of DCT and Gabor wavelet dictionary. The numerical results show that the performance of our algorithm is more efficient in medical image denoising. Keywordsrepresentation (SR), K-SVD, log-Gabor wavelet dictionary, regularized orthogonal matching pursuit and orthogonal matching pursuit.

A new ISR method based on the combination of modified K-SVD model and RAMP algrithm

A new Image Super-resolution Reconstruction (ISR) method combined a modified K-means based Singular Value Decomposition (M_K-SVD) model and Regularized Adaptive Matching Pursuit (RAMP) algorithm is proposed in this paper. In the M_K-SVD model, the maximum sparsity of sparse coefficients is considered. In the condition of the unknown sparsity of the original signals, RAMP algorithm can choose automatically and adaptively the candidate set, and utilize the regularization process to implement the final support set so as to finish accurately the task of signal reconstruction. Combined the advantages of M_K-SVD and RAMP algorithm, for LR images and High Resolution (HR) images, the LR and HR dictionaries are trained. And then, utilized the optimized LR sparse coefficient vectors and the HR dictionary, the HR image patches can be estimated. And considered the original locations of HR image patches to be restored, the LR images can be reconstructed. However, LR images contain much unknown noise, so, before training dictionaries, the LR images are first preprocessed by M_K-SVD model. In test, human-made LR images (i.e. natural images׳ degraded versions) and real LR images (i.e. millimeter wave images, MMW) are respectively used to testify our method proposed. Further, compared our ISR method with those of the basic K-SVD, Regularized Orthogonal Matching Pursuit (ROMP), RAMP, and Sparsity Adaptive Matching Pursuit (SAMP) and so on, experimental results testified the ISR validity of our method proposed. Meanwhile, the Signal Noise Ratio (SNR) criterion is used to measure restored human-made LR images, and the Relative Signal Noise Ratio (RSNR) criterion is used to test the quality of MMW image restored. Experimental results prove that our method is indeed efficient in the research field of ISR reconstruction.