the focus of this paper is to consider the compressed sensing problem. it is stated that the compressed sensing theory, under certain conditions, helps relax the nyquist sampling theory and takes smaller samples. one of the important tasks in this theory is to carefully design measurement matrix (sampling operator). most existing methods in the literature attempt to optimize a randomly initiali...

The null space condition of sensing matrices plays an important role in guaranteeing the success of compressed sensing. In this paper, we propose new efficient algorithms to verify the null space condition in compressed sensing (CS). Given an (n − m) × n (m > 0) CS matrix A and a positive k, we are interested in computing αk = max {z:Az=0,z ̸=0} max {K:|K|≤k} ∥zK∥1 ∥z∥1 , where K represents subs...

Introduction: Compressed sensing (CS) is an acquisition and reconstruction technique that can reduce the measurement size [1]. In this work, we present a novel way to efficiently combine CS and parallel imaging (PI) by separating the estimation methods in k-space. We apply CS to estimate high-frequency k-space data, and use ARC (Autocalibrated Reconstruction for Cartesian sampling) PI to estima...

Optical-resolution photoacoustic microscopy is becoming a powerful research tool for studying microcirculation in vivo. Moreover, ultrasonic-array-based optical-resolution photoacoustic computed tomography (OR-PACT), providing comparable resolution at an improved speed, has opened up new opportunities for studying microvascular dynamics. In this Letter, we have developed a compressed sensing wi...

This paper proposes a new joint decoding algorithm frame based on compressed sensing CS and LDPC (Low-Density Parity-Check) codes. Redundant information can be effectively extracted and amplified by CS reconstruction as a compensation to correct decoding of LDPC codes. We adopt Gaussian kernel function of image segmentation as a reflection. Simulation results indicate, compared with LDPC algori...

The reconstruction of an unknown temporal-spatial profile from participatory sensing data poses a number of challenges due to uncoordinated user movement and possibly low user involvement. This paper considers the problem of reconstructing such a profile from participatory sensing data by exploiting the theory of compressive sensing. In particular we study the impact of the number of users and ...

In this paper, we propose clipping noise cancellation scheme using compressed sensing (CS) for orthogonal frequency division multiplexing (OFDM) systems. In the proposed scheme, only the data tones with high reliability are exploited in reconstructing the clipping noise instead of the whole data tones. For reconstructing the clipping noise using a fraction of the data tones at the receiver, the...

Background Phase contrast (PC) MR is routinely used to quantify blood flow in postnatal subjects and through the use of metric optimized gating (MOG) has been employed in studies of fetal blood flow in both normal pregnancies and fetal congenital heart disease [1-3]. Still, the scan time required for high resolution fetal PCMR remains a practical limitation. Recently, compressed sensing (CS) ha...

This study presents a compressed sensing (CS) based sampling approach for repetitive ultrasonic signal. Proposed system considers recovering ultrasonic signal with high equivalent sampling frequency from samples captured using analog-to-digital converter (ADC) clocked at a rate lower than Nyquist rate. A basis function is constructed to realize ultrasonic signal sparse representation, which pav...

The novel theory of Compressed Sensing (CS) reduces the samples of compressible signal sharply by information sampling. In order to improve reconstruction accuracy of noise signal for CS, a Singular Value Decomposition (SVD) noise signal reconstruction algorithm is presented in this paper. This algorithm decomposes the random measurement matrix, modifies the diagonal matrix Eigen values by mean...