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Manchanda, R., Sharma, K..  2020.  A Review of Reconstruction Algorithms in Compressive Sensing. 2020 International Conference on Advances in Computing, Communication Materials (ICACCM). :322–325.
Compressive Sensing (CS) is a promising technology for the acquisition of signals. The number of measurements is reduced by using CS which is needed to obtain the signals in some basis that are compressible or sparse. The compressible or sparse nature of the signals can be obtained by transforming the signals in some domain. Depending on the signals sparsity signals are sampled below the Nyquist sampling criteria by using CS. An optimization problem needs to be solved for the recovery of the original signal. Very few studies have been reported about the reconstruction of the signals. Therefore, in this paper, the reconstruction algorithms are elaborated systematically for sparse signal recovery in CS. The discussion of various reconstruction algorithms in made in this paper will help the readers in order to understand these algorithms efficiently.
Chandrala, M S, Hadli, Pooja, Aishwarya, R, Jejo, Kevin C, Sunil, Y, Sure, Pallaviram.  2019.  A GUI for Wideband Spectrum Sensing using Compressive Sampling Approaches. 2019 10th International Conference on Computing, Communication and Networking Technologies (ICCCNT). :1–6.
Cognitive Radio is a prominent solution for effective spectral resource utilization. The rapidly growing device to device (D2D) communications and the next generation networks urge the cognitive radio networks to facilitate wideband spectrum sensing in order to assure newer spectral opportunities. As Nyquist sampling rates are formidable owing to complexity and cost of the ADCs, compressive sampling approaches are becoming increasingly popular. One such approach exploited in this paper is the Modulated Wideband Converter (MWC) to recover the spectral support. On the multiple measurement vector (MMV) framework provided by the MWC, threshold based Orthogonal Matching Pursuit (OMP) and Sparse Bayesian Learning (SBL) algorithms are employed for support recovery. We develop a Graphical User Interface (GUI) that assists a beginner to simulate the RF front-end of a MWC and thereby enables the user to explore support recovery as a function of Signal to Noise Ratio (SNR), number of measurement vectors and threshold. The GUI enables the user to explore spectrum sensing in DVB-T, 3G and 4G bands and recovers the support using OMP or SBL approach. The results show that the performance of SBL is better than that of OMP at a lower SNR values.
Wen, Jinming, Yu, Wei.  2019.  Exact Sparse Signal Recovery via Orthogonal Matching Pursuit with Prior Information. ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). :5003–5007.
The orthogonal matching pursuit (OMP) algorithm is a commonly used algorithm for recovering K-sparse signals x ∈ ℝn from linear model y = Ax, where A ∈ ℝm×n is a sensing matrix. A fundamental question in the performance analysis of OMP is the characterization of the probability that it can exactly recover x for random matrix A. Although in many practical applications, in addition to the sparsity, x usually also has some additional property (for example, the nonzero entries of x independently and identically follow the Gaussian distribution), none of existing analysis uses these properties to answer the above question. In this paper, we first show that the prior distribution information of x can be used to provide an upper bound on \textbackslashtextbar\textbackslashtextbarx\textbackslashtextbar\textbackslashtextbar21/\textbackslashtextbar\textbackslashtextbarx\textbackslashtextbar\textbackslashtextbar22, and then explore the bound to develop a better lower bound on the probability of exact recovery with OMP in K iterations. Simulation tests are presented to illustrate the superiority of the new bound.
Brodeur, S., Rouat, J..  2017.  Optimality of inference in hierarchical coding for distributed object-based representations. 2017 15th Canadian Workshop on Information Theory (CWIT). :1–5.

Hierarchical approaches for representation learning have the ability to encode relevant features at multiple scales or levels of abstraction. However, most hierarchical approaches exploit only the last level in the hierarchy, or provide a multiscale representation that holds a significant amount of redundancy. We argue that removing redundancy across the multiple levels of abstraction is important for an efficient representation of compositionality in object-based representations. With the perspective of feature learning as a data compression operation, we propose a new greedy inference algorithm for hierarchical sparse coding. Convolutional matching pursuit with a L0-norm constraint was used to encode the input signal into compact and non-redundant codes distributed across levels of the hierarchy. Simple and complex synthetic datasets of temporal signals were created to evaluate the encoding efficiency and compare with the theoretical lower bounds on the information rate for those signals. Empirical evidence have shown that the algorithm is able to infer near-optimal codes for simple signals. However, it failed for complex signals with strong overlapping between objects. We explain the inefficiency of convolutional matching pursuit that occurred in such case. This brings new insights about the NP-hard optimization problem related to using L0-norm constraint in inferring optimally compact and distributed object-based representations.

H. Kiragu, G. Kamucha, E. Mwangi.  2015.  "A fast procedure for acquisition and reconstruction of magnetic resonance images using compressive sampling". AFRICON 2015. :1-5.

This paper proposes a fast and robust procedure for sensing and reconstruction of sparse or compressible magnetic resonance images based on the compressive sampling theory. The algorithm starts with incoherent undersampling of the k-space data of the image using a random matrix. The undersampled data is sparsified using Haar transformation. The Haar transform coefficients of the k-space data are then reconstructed using the orthogonal matching Pursuit algorithm. The reconstructed coefficients are inverse transformed into k-space data and then into the image in spatial domain. Finally, a median filter is used to suppress the recovery noise artifacts. Experimental results show that the proposed procedure greatly reduces the image data acquisition time without significantly reducing the image quality. The results also show that the error in the reconstructed image is reduced by median filtering.

Liang Zhongyin, Huang Jianjun, Huang Jingxiong.  2015.  "Sub-sampled IFFT based compressive sampling". TENCON 2015 - 2015 IEEE Region 10 Conference. :1-4.

In this paper, a new approach based on Sub-sampled Inverse Fast Fourier Transform (SSIFFT) for efficiently acquiring compressive measurements is proposed, which is motivated by random filter based method and sub-sampled FFT. In our approach, to start with, we multiply the FFT of input signal and that of random-tap FIR filter in frequency domain and then utilize SSIFFT to obtain compressive measurements in the time domain. It requires less data storage and computation than the existing methods based on random filter. Moreover, it is suitable for both one-dimensional and two-dimensional signals. Experimental results show that the proposed approach is effective and efficient.