Orthogonal Matching Pursuit

We propose the audio inpainting framework that recovers portions of audio data distorted due to impairments such as impulsive noise, clipping, and packet loss. In this framework, the distorted data are treated as missing and their location is assumed to be known. The signal is decomposed into overlapping time-domain frames and the restoration problem is then formulated as an inverse problem per audio frame. Sparse representation modeling is employed per frame, and each inverse problem is solved using the Orthogonal Matching Pursuit algorithm together with a discrete cosine or a Gabor dictionary. The Signal-to-Noise Ratio performance of this algorithm is shown to be comparable or better than state-of-the-art methods when blocks of samples of variable durations are missing. We also demonstrate that the size of the block of missing samples, rather than the overall number of missing samples, is a crucial parameter for high quality signal restoration. We further introduce a constrained Matching Pursuit approach for the special case of audio declipping that exploits the sign pattern of clipped audio samples and their maximal absolute value, as well as allowing the user to specify the maximum amplitude of the signal. This approach is shown to outperform state-of-the-art and commercially available methods for audio declipping in terms of Signal-to-Noise Ratio.

—Compressive sensing system merges sampling and compression for a given sparse signal. It can reconstruct the image accurately by using fewer linear measurements than the original measurements. Hence, it is able to achieve reduction in complexity of sampling and number of computations. Since existing algorithms for implementation of sampling for the whole image are time consuming and it requires huge storage space, greedy approaches are used commonly to recover sparse signals from fewer measurements. One of the commonly used greedy approaches is Orthogonal Matching Pursuit (OMP), which can iteratively reconstruct the image. In this paper, modified form of OMP is presented in which stopping condition specified by the Recovery condition and Mutual incoherence property is used on the low frequency coefficients of the image. The simulation result using modified OMP shows that the reconstructed image achieves better PSNR and uses lesser number of measurements.

Polytope Faces Pursuit (PFP) is a greedy algorithm that approximates the sparse solutions recovered by ℓ1 regularised least-squares (Lasso) [4,10] in a similar vein to (Orthogonal) Matching Pursuit (OMP) [16]. The algorithm is based on the geometry of the polar polytope where at each step a basis function is chosen by finding the maximal vertex using a path-following method. The algorithmic complexity is of a similar order to OMP whilst being able to solve problems known to be hard for (O)MP. Matching Pursuit was extended to build kernel-based solutions to machine learning problems, resulting in the sparse regression algorithm, Kernel Matching Pursuit (KMP) [17]. We develop a new algorithm to build sparse kernel-based solutions using PFP, which we call Kernel Polytope Faces Pursuit (KPFP). We show the usefulness of this algorithm by providing a generalisation error bound [7] that takes into account a natural regression loss and experimental results on several benchmark datasets.

A novel technique for despeckling the medical ultrasound images using lossy compression is presented. The logarithm of the input image is first transformed to the multiscale wavelet domain. It is then shown that the subband coefficients of the log-transformed ultrasound image can be successfully modeled using the generalized Laplacian distribution. Based on this modeling, a simple adaptation of the zero-zone and reconstruction levels of the uniform threshold quantizer is proposed in order to achieve simultaneous despeckling and quantization. This adaptation is based on: 1) an estimate of the corrupting speckle noise level in the image; 2) the estimated statistics of the noise-free subband coefficients; and 3) the required compression rate. The Laplacian distribution is considered as a special case of the generalized Laplacian distribution and its efficacy is demonstrated for the problem under consideration. Context-based classification is also applied to the noisy coefficients to enhance the performance of the subband coder. Simulation results using a contrast detail phantom image and several real ultrasound images are presented. To validate the performance of the proposed scheme, comparison with two two-stage schemes, wherein the speckled image is first filtered and then compressed using the state-of-the-art JPEG2000 encoder, is presented. Experimental results show that the proposed scheme works better, both in terms of the signal to noise ratio and the visual quality.

Many algorithms have been developed to find sparse representation over redundant dictionaries or transform. This paper presents a novel method on compressive sensing (CS)-based image compression using sparse basis on CDF9/7 wavelet transform. The measurement matrix is applied to the three levels of wavelet transform coefficients of the input image for compressive sampling. We have used three different measurement matrix as Gaussian matrix, Bernoulli measurement matrix and random orthogonal matrix. The orthogonal matching pursuit (OMP) and Basis Pursuit (BP) are applied to reconstruct each level of wavelet transform separately. Experimental results demonstrate that the proposed method given better quality of compressed image than existing methods in terms of proposed image quality evaluation indexes and other objective (PSNR/UIQI/SSIM) measurements.

In cognitive radio (CR) networks, unlicensed (cognitive) users can exploit the licensed frequency bands by using spectrum sensing techniques to identify spectrum holes. This paper proposes a distributed compressive spectrum sensing scheme, in which the modulated wide-band converter can apply compressed sensing (CS) directly to analog signals at the sub-Nyquist rate and the central fusion receives signals from multiple CRs and exploits the multiple-measurements-vectors (MMV) subspace pursuit (M-SP) algorithm to jointly reconstruct the spectral support of the wide-band signal. This support is then used to detect whether the licensed bands are occupy or not. Finally, extensive simulation results show the advantages of the proposed scheme. Besides, we also compare the performance of M-SP with M-orthogonal matching pursuit (M-OMP) algorithms.

This report studies the eect of introducing a priori knowledge to recover sparse representations when overcomplete dictionaries are used. We focus mainly on Greedy algorithms and Basis Pursuit as for our algorithmic basement, while a priori is incorporated by suitably weighting the elements of the dictionary. A unique sucien t condition is provided under which Orthogonal Matching Pursuit, Matching Pursuit

Many algorithms have been developed to find sparse representation over redundant dictionaries or transform. This paper presents a novel method on compressive sensing (CS)-based image compression using sparse basis on CDF9/7 wavelet transform. The measurement matrix is applied to the three levels of wavelet transform coefficients of the input image for compressive sampling. We have used three different measurement matrix as Gaussian matrix, Bernoulli measurement matrix and random orthogonal matrix. The orthogonal matching pursuit (OMP) and Basis Pursuit (BP) are applied to reconstruct each level of wavelet transform separately. Experimental results demonstrate that the proposed method given better quality of compressed image than existing methods in terms of proposed image quality evaluation indexes and other objective (PSNR/UIQI/SSIM) measurements.

This paper considers compressed sensing (CS) techniques for signal reconstruction and channel estimation in OFDM-based high-rate ultra wideband (UWB) communication systems. We employ a parallel CS structure that exploits frequency domain sparsity. We also consider multipath UWB channels in both the line-of-sight and non line-of-sight environments. UWB signal detection and channel estimation from sub-Nyquist analog projections is carried out using an optimized orthogonal matching pursuit algorithm and the smoothed ℓ0 algorithm. Simulation results demonstrate significant gains in the form of reliable signal recovery and channel estimation as well as dramatically sub-Nyquist sampling rates for the analog-to-digital converters while maintaining high data rates.

Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design

Recovery algorithms play a key role in compressive sampling (CS). Currently, a popular recovery algorithm for CS is the orthogonal matching pursuit (OMP), which possesses the merits of low complexity and good recovery quality. Considering that the OMP involves massive matrix/vector operations, it is very suited to being implemented in parallel on graphics processing unit (GPU). In this paper, we

Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design

RESUMEN Muestreo compresivo es una rama emergente del procesamiento de señales, basada en el hecho de que un número pequeño de proyecciones lineales no adaptativas sobre una señal compresible contiene suficiente información para reconstruirla y ...

This paper considers a simple on-off random multiple access channel, where n users communicate simultaneously to a single receiver over m degrees of freedom. Each user transmits with probability lambda, where typically lambda n < m << n, and the receiver must detect which users transmitted. We show that when the codebook has i.i.d. Gaussian entries, detecting which users transmitted is mathematically equivalent to a certain sparsity detection problem considered in compressed sensing. Using recent sparsity results, we derive upper and lower bounds on the capacities of these channels. We show that common sparsity detection algorithms, such as lasso and orthogonal matching pursuit (OMP), can be used as tractable multiuser detection schemes and have significantly better performance than single-user detection. These methods do achieve some near-far resistance but--at high signal-to-noise ratios (SNRs)--may achieve capacities far below optimal maximum likelihood detection. We then present a new algorithm, called sequential OMP, that illustrates that iterative detection combined with power ordering or power shaping can significantly improve the high SNR performance. Sequential OMP is analogous to successive interference cancellation in the classic multiple access channel. Our results thereby provide insight into the roles of power control and multiuser detection on random-access signalling.