Subsampling Schemes Research Articles

Two-phase designs with failure time processes subject to nonsusceptibility.

Epidemiological studies based on 2-phase designs help ensure efficient use of limited resources in situations where certain covariates are prohibitively expensive to measure for a full cohort. Typically, these designs involve 2 steps: In phase I, data on an outcome and inexpensive covariates are acquired, and in phase II, a subsample is chosen in which the costly variable of interest is measured. For right-censored data, 2-phase designs have been primarily based on the Cox model. We develop efficient 2-phase design strategies for settings involving a fraction of long-term survivors due to nonsusceptibility. Using mixture models accommodating a nonsusceptible fraction, we consider 3 regression frameworks, including (a) a logistic "cure" model, (b) a proportional hazards model for those who are susceptible, and (c) regression models for susceptibility and failure time in those susceptible. Importantly, we introduce a novel class of bivariate residual-dependent designs to address the unique challenges presented in scenario (c), which involves 2 parameters of interest. Extensive simulation studies demonstrate the superiority of our approach over various phase II subsampling schemes. We illustrate the method through applications to the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial.

On retrospective k-space subsampling schemes for deep MRI reconstruction

Acquiring fully-sampled MRI k-space data is time-consuming, and collecting accelerated data can reduce the acquisition time. Employing 2D Cartesian-rectilinear subsampling schemes is a conventional approach for accelerated acquisitions; however, this often results in imprecise reconstructions, even with the use of Deep Learning (DL), especially at high acceleration factors. Non-rectilinear or non-Cartesian trajectories can be implemented in MRI scanners as alternative subsampling options. This work investigates the impact of the k-space subsampling scheme on the quality of reconstructed accelerated MRI measurements produced by trained DL models. The Recurrent Variational Network (RecurrentVarNet) was used as the DL-based MRI-reconstruction architecture. Cartesian, fully-sampled multi-coil k-space measurements from three datasets were retrospectively subsampled with different accelerations using eight distinct subsampling schemes: four Cartesian-rectilinear, two Cartesian non-rectilinear, and two non-Cartesian. Experiments were conducted in two frameworks: scheme-specific, where a distinct model was trained and evaluated for each dataset-subsampling scheme pair, and multi-scheme, where for each dataset a single model was trained on data randomly subsampled by any of the eight schemes and evaluated on data subsampled by all schemes. In both frameworks, RecurrentVarNets trained and evaluated on non-rectilinearly subsampled data demonstrated superior performance, particularly for high accelerations. In the multi-scheme setting, reconstruction performance on rectilinearly subsampled data improved when compared to the scheme-specific experiments. Our findings demonstrate the potential for using DL-based methods, trained on non-rectilinearly subsampled measurements, to optimize scan time and image quality.

Enumeration of microparticles on a gridded filter using a stratified random sampling tool

Quantifying microplastics and other microparticles is a matter of interest in the field of environmental science. Stereomicroscopy is one of the most common methods to identify and enumerate micro-size particles. However, the process of enumerating an entire environmental sample can be tedious and time-consuming, especially when target particles are abundant. Here we present a method to develop a subsampling strategy and spreadsheet-based tool to speed up the process of microparticle enumeration while maintaining particle count accuracy. We first identified the pattern in which tire road wear particles (TRWPs) from environmental samples were distributed on a filter when vacuum-plated, then used particle abundance within relatively homogeneous subsection arrangements to establish stratified random subsampling schemes. We describe a repeated sampling experiment using count data to test the stratified design and illustrate the relationship between the fraction of the filter counted (sample size) with accuracy and variance in the extrapolated total sample count and the corresponding analyst time savings when applied to analyzing TRWPs isolated from sediments. Based on the results, a particle enumeration tool was created in Microsoft Excel Visual BasicⓇ configured using a 47 mm gridded filter, and the source is available for free modification under the same open license.•Vacuum-plated microparticles are often highly abundant and not homogenously distributed across a filter.•A random sampling selection data tool was created using knowledge of particle distribution.•Method describes how to structure and use partial filter counts to extrapolate for total particle enumeration.

On the sampling strategies and models for measuring diffusion exchange with a double diffusion encoding sequence

Water exchange between the different compartments of a heterogeneous specimen can be characterized via diffusion magnetic resonance imaging (dMRI). Many analysis frameworks using dMRI data have been proposed to describe exchange, often using a double diffusion encoding (DDE) stimulated echo sequence. Techniques such as diffusion exchange weighted imaging (DEWI) and the filter exchange and rapid exchange models, use a specific subset of the full space DDE signal. In this work, a general representation of the DDE signal was employed with different sampling schemes (namely constant b1, diagonal and anti-diagonal) from the data reduction models to estimate exchange. A near-uniform sampling scheme was proposed and compared with the other sampling schemes. The filter exchange and rapid exchange models were also applied to estimate exchange with their own subsampling schemes. These subsampling schemes and models were compared on both simulated data and experimental data acquired with a benchtop MR scanner. In synthetic data, the diagonal and near-uniform sampling schemes performed the best due to the consistency of their estimates with the ground truth. In experimental data, the shifted diagonal and near-uniform sampling schemes outperformed the others, yielding the most consistent estimates with the full space estimation. The results suggest the feasibility of measuring exchange using a general representation of the DDE signal along with variable sampling schemes. In future studies, algorithms could be further developed for the optimization of sampling schemes, as well as incorporating additional properties, such as geometry and diffusion anisotropy, into exchange frameworks.

Multi-coil MRI by analytic continuation

Abstract We present novel reconstruction and stability analysis methodologies for two-dimensional, multi-coil MRI, based on analytic continuation ideas. We show that the 2-D, limited-data MRI inverse problem, whereby the missing parts of 𝐤 {\mathbf{k}} -space (Fourier space) are lines parallel to either k 1 {k_{1}} or k 2 {k_{2}} (i.e., the 𝐤 {\mathbf{k}} -space axis), can be reduced to a set of 1-D Fredholm type inverse problems. The Fredholm equations are then solved to recover the 2-D image on 1-D line profiles (“slice-by-slice” imaging). The technique is tested on a range of medical in vivo images (e.g., brain, spine, cardiac), and phantom data. Our method is shown to offer optimal performance, in terms of structural similarity, when compared against similar methods from the literature, and when the 𝐤 {\mathbf{k}} -space data is sub-sampled at random so as to simulate motion corruption. In addition, we present a Singular Value Decomposition (SVD) and stability analysis of the Fredholm operators, and compare the stability properties of different 𝐤 {\mathbf{k}} -space sub-sampling schemes (e.g., random vs uniform accelerated sampling).

Point Cloud Sampling via Graph Balancing and Gershgorin Disc Alignment.

Point cloud (PC)-a collection of discrete geometric samples of a 3D object's surface-is typically large, which entails expensive subsequent operations. Thus, PC sub-sampling is of practical importance. Previous model-based sub-sampling schemes are ad-hoc in design and do not preserve the overall shape sufficiently well, while previous data-driven schemes are trained for specific pre-determined input PC sizes and sub-sampling rates and thus do not generalize well. Leveraging advances in graph sampling, we propose a fast PC sub-sampling algorithm of linear time complexity that chooses a 3D point subset while minimizing a global reconstruction error. Specifically, to articulate a sampling objective, we first assume a super-resolution (SR) method based on feature graph Laplacian regularization (FGLR) that reconstructs the original high-res PC, given points chosen by a sampling matrix H. We prove that minimizing a worst-case SR reconstruction error is equivalent to maximizing the smallest eigenvalue λmin of matrix HT H+ μL, where L is a symmetric, positive semi-definite matrix derived from a neighborhood graph connecting the 3D points. To arrive at a fast algorithm, instead of maximizing λmin, we maximize a lower bound λ-min(HT H+ μL) via selection of H-this translates to a graph sampling problem for a signed graph G with self-loops specified by graph Laplacian L. We tackle this general graph sampling problem in three steps. First, we approximate G with a balanced graph GB specified by Laplacian LB. Second, leveraging a recent linear algebraic theorem called Gershgorin disc perfect alignment (GDPA), we perform a similarity transform Lp = SLB S-1, so that all Gershgorin disc left-ends of Lp are aligned exactly at λmin(LB). Finally, we choose samples on GB using a previous graph sampling algorithm to maximize λ-min(HT H+ μLp) in linear time. Experimental results show that 3D points chosen by our algorithm outperformed competing schemes both numerically and visually in reconstruction quality.

Unweighted estimation based on optimal sample under measurement constraints

AbstractTo tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling approach under measurement constraints was developed to meet this challenge. This method uses the inverses of optimal sampling probabilities to reweight the objective function, which assigns smaller weights to the more important data points. Thus, the estimation efficiency of the resulting estimator can be improved. In this paper, we propose an unweighted estimating procedure based on optimal subsamples to obtain a more efficient estimator. We obtain the unconditional asymptotic distribution of the estimator via martingale techniques without conditioning on the pilot estimate, which has been less investigated in the existing subsampling literature. Both asymptotic results and numerical results show that the unweighted estimator is more efficient in parameter estimation.

Impacts of sampling frequency on the estimation accuracy of exceedance for suspended solids and nitrates in streams in small to medium-sized watersheds

Data from a 389 km2 watershed and one of its 14.5 km2 subbasins were used to assess the effects of sampling frequency on the estimation accuracy of the exceedance frequency (EF) for suspended solids and nitrate-nitrogen in streams. Values of EF estimated from 17 subsampling schemes were compared with the actual EF (EFa) at different threshold concentrations. The coefficient of variation and relative bias were used to measure the estimation accuracy. Results indicated that the EFa of the larger watershed was much lower than that of the smaller watershed for both suspended solids and nitrate-nitrogen. We also found that EFa can be modeled as an exponential function of the threshold concentration. For the EF estimations, the coefficient of variation decreased with increasing sampling frequency and increasing EFa. The relative bias tended to be negative when EFa was low or the threshold concentration was high, reaching -75% in some cases. This result implies that reported EF values based on low-frequency data could be severely underestimated due to the high possibility of missing large events. However, there were also cases with positive relative bias, implying overestimation of EF due to over representation of large events. These findings can be used to determine adequate sampling frequencies for water-quality parameters, avoiding common observed biases (mostly negative) in the estimation of EF for extreme pollution events.

Assessment of Subsampling Schemes for Compressive Nano-FTIR Imaging

Nano-FTIR imaging is a powerful scanning-based technique at nanometer spatial resolution that combines Fourier transform infrared spectroscopy (FTIR) and scattering-type scanning near-field optical microscopy (s-SNOM). Recording large spatial areas using nano-FTIR is, however, limited because its sequential data acquisition entails long measurement times. Compressed sensing and low-rank matrix reconstruction are mathematical techniques that can reduce the number of these measurements significantly by requiring only a small fraction of randomly chosen measurements. However, choosing this small set of measurements in a random fashion poses practical challenges for scanning procedures and does not save as much time as desired. We therefore consider different sub-sampling schemes of practical relevance that ensure rapid data acquisition, much faster than random sub-sampling, in combination with a low-rank matrix reconstruction procedure. It is demonstrated that the quality of the results for almost all sub-sampling schemes considered, namely original Lissajous, triangle Lissajous, and random reflection sub-sampling, is similarly to that achieved for random sub-sampling. This implies that nano-FTIR imaging can be significantly extended to also cover samples extended over large areas while maintaining its high spatial resolution.

Locally Optimal Subsampling Strategies for Full Matrix Capture Measurements in Pipe Inspection

In ultrasonic non-destructive testing, array and matrix transducers are being employed for applications that require in-field steerability or which benefit from a higher number of insonification angles. Having many transmit channels, on the other hand, increases the measurement time and renders the use of array transducers unfeasible for many applications. In the literature, methods for reducing the number of required channels compared to the full matrix capture scheme have been proposed. Conventionally, these are based on choosing the aperture that is as wide as possible. In this publication, we investigate a scenario from the field of pipe inspection, where cracks have to be detected in specific areas near the weld. Consequently, the width of the aperture has to be chosen according to the region of interest at hand. On the basis of ray-tracing simulations which incorporate a model of the transducer directivity and beam spread at the interface, we derive application specific measures of the energy distribution over the array configuration for given regions of interest. These are used to determine feasible subsampling schemes. For the given scenario, the validity/quality of the derived subsampling schemes are compared on the basis of reconstructions using the conventional total focusing method as well as sparsity driven-reconstructions using the Fast Iterative Shrinkage-Thresholding Algorithm. The results can be used to effectively improve the measurement time for the given application without notable loss in defect detectability.

Subsampled digital holographic image reconstruction by a compressive sensing approach.

We show an in-line digital holographic image reconstruction from subsampled holograms with resolution improvement and lensless magnification with high noise immunity by a compressive sensing approach. Our method treats the sensed field as subsampled, low-pass filtered and projected on a Fresnel-Bluestein base in an inverse problem approach to image reconstruction with controlled lensless magnification. So, we have demonstrated by simulation and experimental results that the approach can reconstruct images with quality even when used in holograms obtained from unusual subsampling schemes.

Biogeographical and analytical implications of temporal variability in geographically diverse soundscapes

Unprecedented rates of biodiversity loss and intensifying human attempts to rectify the biodiversity crisis have heightened the need for standardized, large-scale, long-duration biodiversity monitoring at fine temporal resolution. While some innovative technologies such as passive acoustic monitoring are well suited for such monitoring challenges, many questions remain as to how they should be scaled out and optimally implemented across ecosystems.Our research questions center on temporal sampling regimes—how frequently and how long one should collect data to represent biodiversity conditions over a given timeframe. Addressing this concern in the context of passive acoustic monitoring, we investigated whether temporal soundscape variability—the characteristic short-term acoustic change in an environment—is consistent across ecosystems and times of day, and we considered how various temporal subsampling schemes affect the representativeness of resultant acoustic index values, relative to continuous sampling. We quantified soundscape variability at eight sites across four continents based on temporal autocorrelation ranges and standard deviations of acoustic index values, and we created a heuristic model to classify types of soundscape variability based on those two variables.Drawing on values derived from three distinct acoustic indices, we found that the characteristic temporal variability of soundscapes varied between sites and times of day (dawn, daytime, dusk, and nighttime). Some sites exhibited little difference in variability between times of day whereas other sites exhibited greater within-site differences between times of day than many inter-site differences. Daytime soundscapes generally tended to exhibit more temporal variability than nighttime soundscapes.We also compared potential subsampling schemes that could be advantageous in terms of power, data storage, and data analysis costs by modeling subsample error as a function of total analysis time and number of subsamples within a larger block of time. Greater numbers of evenly distributed subdivisions drastically increased the representativeness of a sampling scheme, while increases in subsample duration yielded fairly minimal gains in representativeness between 33 and 67% of the full time one wishes to represent. Generally, our results show that for a long-term, fine temporal resolution monitoring program, one should record in evenly distributed durations at least as short as 1 min while only recording up to a third of the time one wishes to represent. While more continuous monitoring can be advantageous and necessary in many cases, current economic and logistical limitations in power, data storage, and analysis capabilities will often warrant optimized subsampling designs.

CORE-Deblur: Parallel MRI Reconstruction by Deblurring using compressed sensing

In this work we introduce a new method that combines Parallel MRI and Compressed Sensing (CS) for accelerated image reconstruction from subsampled k-space data. The method first computes a convolved image, which gives the convolution between a user-defined kernel and the unknown MR image, and then reconstructs the image by CS-based image deblurring, in which CS is applied for removing the inherent blur stemming from the convolution process. This method is hence termed CORE-Deblur. Retrospective subsampling experiments with data from a numerical brain phantom and in-vivo 7T brain scans showed that CORE-Deblur produced high-quality reconstructions, comparable to those of a conventional CS method, while reducing the number of iterations by a factor of 10 or more. The average Normalized Root Mean Square Error (NRMSE) obtained by CORE-Deblur for the in-vivo datasets was 0.016. CORE-Deblur also exhibited robustness regarding the chosen kernel and compatibility with various k-space subsampling schemes, ranging from regular to random. In summary, CORE-Deblur enables high quality reconstructions and reduction of the CS iterations number by 10-fold.

Optimal bias correction of the log-periodogram estimator of the fractional parameter: A jackknife approach

We use the jackknife to bias correct the log-periodogram regression (LPR) estimator of the fractional parameter in a stationary fractionally integrated model. The weights for the jackknife estimator are chosen in such a way that bias reduction is achieved without the usual increase in asymptotic variance, with the estimator viewed as ‘optimal’ in this sense. The theoretical results are valid under both the non-overlapping and moving-block sub-sampling schemes that can be used in the jackknife technique, and do not require the assumption of Gaussianity for the data generating process. A Monte Carlo study explores the finite sample performance of different versions of the jackknife estimator, under a variety of scenarios. The simulation experiments reveal that when the weights are constructed using the parameter values of the true data generating process, a version of the optimal jackknife estimator almost always out-performs alternative semi-parametric bias-corrected estimators. A feasible version of the jackknife estimator, in which the weights are constructed using estimates of the unknown parameters, whilst not dominant overall, is still the least biased estimator in some cases. Even when misspecified short run dynamics are assumed in the construction of the weights, the feasible jackknife estimator still shows significant reduction in bias under certain designs. As is not surprising, parametric maximum likelihood estimation out-performs all semi-parametric methods when the true values of the short memory parameters are known, but is dominated by the semi-parametric methods (in terms of bias) when the short memory parameters need to be estimated, and in particular when the model is misspecified.

Bootstrapping M-estimators in generalized autoregressive conditional heteroscedastic models

Summary We consider the weighted bootstrap approximation to the distribution of a class of M-estimators for the parameters of the generalized autoregressive conditional heteroscedastic model. We prove that the bootstrap distribution, given the data, is a consistent estimate in probability of the distribution of the M-estimator, which is asymptotically normal. We propose an algorithm for the computation of M-estimates which at the same time is useful for computing bootstrap replicates from the given data. Our simulation study indicates superior coverage rates for various weighted bootstrap schemes compared with the rates based on the normal approximation and existing bootstrap methods for the generalized autoregressive conditional heteroscedastic model, such as percentile $t$-subsampling schemes. Since some familiar bootstrap schemes are special cases of the weighted bootstrap, this paper thus provides a unified theory and algorithm for bootstrapping in generalized autoregressive conditional heteroscedastic models.

A Simulation Study to Evaluate Biases in Population Characteristics Estimation Associated with Varying Bin Numbers in Size‐Based Age Subsampling

AbstractIn temperate waters, growth and mortality of bony fishes are frequently estimated from age information derived from the examination of annular rings on hard structures (e.g., otoliths). However, determining ages from hard structures can be time consuming, often requires sacrificing fish, and has associated costs for supplies and personnel time in processing or reading structures. Subsampling based on a target number of fish per length bin is commonly used to reduce time and costs but may introduce biases into the estimation of population characteristics. We wanted to understand how interactive effects of bin width, gear selectivity, and length‐at‐age variability influence the estimation of growth parameters, total instantaneous mortality (Z), and age frequency. We developed a simulation model to generate populations under the assumption that growth followed the von Bertalanffy growth model; we then sampled from those populations for age analysis based on no gear selectivity, dome‐shaped selectivity, and logistic selectivity. Furthermore, we wanted to determine whether observed biases could be corrected by using a weighting procedure during growth model fitting. Fifteen subsampling schemes were evaluated, with five different length bin widths and three target subsample sizes for each bin (subsampling levels). Gear selectivity, variability in length at age, and estimation procedures had a greater and more predictable influence on growth parameters than bin widths for size‐based subsampling. Dome‐shaped gear selectivity was associated with biases in growth parameter and Z estimation. Weighted regression based on weighting factors calculated from the original sample's length frequency generally improved the consistency of growth parameter estimates among subsampling schemes but did not always improve accuracy. No bin widths or subsample sizes were clearly superior across modeled scenarios. Consequently, alteration of bin widths seems less useful in reducing biases than using alternative estimation methods for population characteristics of interest and considering other external factors.

Biogeographical and analytical implications of temporal variability in geographically diverse soundscapes

• Continuous soundscape recordings were made in eight ecosystems on four continents. • Temporal variability of soundscapes was quantified using two distinct measures. • Daytime exhibited high temporal variability relative to dusk and nighttime. • Increasing evenness of subsampling distribution reduces error in representation. • Marginal precision gains diminish substantially beyond 1/3 recording time. Unprecedented rates of biodiversity loss and intensifying human attempts to rectify the biodiversity crisis have heightened the need for standardized, large-scale, long-duration biodiversity monitoring at fine temporal resolution. While some innovative technologies such as passive acoustic monitoring are well suited for such monitoring challenges, many questions remain as to how they should be scaled out and optimally implemented across ecosystems. Our research questions center on temporal sampling regimes—how frequently and how long one should collect data to represent biodiversity conditions over a given timeframe. Addressing this concern in the context of passive acoustic monitoring, we investigated whether temporal soundscape variability—the characteristic short-term acoustic change in an environment—is consistent across ecosystems and times of day, and we considered how various temporal subsampling schemes affect the representativeness of resultant acoustic index values, relative to continuous sampling. We quantified soundscape variability at eight sites across four continents based on temporal autocorrelation ranges and standard deviations of acoustic index values, and we created a heuristic model to classify types of soundscape variability based on those two variables. Drawing on values derived from three distinct acoustic indices, we found that the characteristic temporal variability of soundscapes varied between sites and times of day (dawn, daytime, dusk, and nighttime). Some sites exhibited little difference in variability between times of day whereas other sites exhibited greater within-site differences between times of day than many inter-site differences. Daytime soundscapes generally tended to exhibit more temporal variability than nighttime soundscapes. We also compared potential subsampling schemes that could be advantageous in terms of power, data storage, and data analysis costs by modeling subsample error as a function of total analysis time and number of subsamples within a larger block of time. Greater numbers of evenly distributed subdivisions drastically increased the representativeness of a sampling scheme, while increases in subsample duration yielded fairly minimal gains in representativeness between 33 and 67% of the full time one wishes to represent. Generally, our results show that for a long-term, fine temporal resolution monitoring program, one should record in evenly distributed durations at least as short as 1 min while only recording up to a third of the time one wishes to represent. While more continuous monitoring can be advantageous and necessary in many cases, current economic and logistical limitations in power, data storage, and analysis capabilities will often warrant optimized subsampling designs.

Bayesian 3D Reconstruction of Subsampled Multispectral Single-Photon Lidar Signals

Light detection and ranging (Lidar) single-photon devices capture range and intensity information from a three-dimensional (3-D) scene. This modality enables long range 3-D reconstruction with high range precision and low laser power. A multispectral single-photon Lidar system provides additional spectral diversity, allowing the discrimination of different materials. However, the main drawback of such systems can be the long acquisition time needed to collect enough photons in each spectral band. In this work, we tackle this problem in two ways: first, we propose a Bayesian 3-D reconstruction algorithm that is able to find multiple surfaces per pixel, using few photons, i.e., shorter acquisitions. In contrast to previous algorithms, the novel method processes jointly all the spectral bands, obtaining better reconstructions using less photon detections. The proposed model promotes spatial correlation between neighbouring points within a given surface using spatial point processes. Secondly, we account for different spatial and spectral subsampling schemes, which reduce the total number of measurements, without significant degradation of the reconstruction performance. In this way, the total acquisition time, memory requirements and computational time can be significantly reduced. The experiments performed using both synthetic and real single-photon Lidar data demonstrate the advantages of tailored sampling schemes over random alternatives. Furthermore, the proposed algorithm yields better estimates than other existing methods for multi-surface reconstruction using multispectral Lidar data.

Sample Efficient Fourier Ptychography for Structured Data

We study the problem of recovering structured data from Fourier ptychography measurements. Fourier ptychography is an image acquisition scheme that uses an array of images to produce high-resolution images in microscopy as well as long-distance imaging, to mitigate the effects of diffraction blurring. The number of measurements is typically much larger than the size of the signal (image or video) to be reconstructed, which translates to high storage and computational requirements. The issue of high sample complexity can be alleviated by utilizing structural properties of the image (or video). In this article, we first discuss a range of sub-sampling schemes which can reduce the amount of measurements in Fourier ptychography setups; however, this makes the problem ill-posed. Correspondingly, we impose structural constraints on the signals to be recovered, to regularize the problem. Through our novel framework of recovery algorithms, we show that one can reconstruct high-resolution images (or video) from fewer samples, via simple and natural assumptions on the structure of the images (or video). We demonstrate the validity of our claims through a series of experiments, both on simulated and real data.

Direction of arrival estimation with missing data via matrix completion

In this paper, we consider the problem of direction of arrival (DOA) estimation on a large sensor array, in the case of missing data resulting from chain failure or employed sub-sampling schemes. Since the missing measurements impair the performance of DOA estimation, we propose to recover the missing entries from the available ones, by applying matrix completion (MC) techniques. We use three well-known MC algorithms SVT, LMaFit, and OptSpace for imputation of the missing entries and then employing MUSIC algorithm to estimate the angles of impinging signals. In addition, we improve the performance of MC techniques, by employing the information theoretic based source enumeration methods, such as MDL and AIC, instead of the heuristic and imprecise rank estimator in current methods. The mean-square error (MSE) of DOA estimation is taken as an assessment criterion for comparing the performance of the aforementioned MC algorithms. Simulation results are conducted to show that in addition to performance improvement achieved by imputation of the missing measurements, the LMaFit algorithm with the proposed rank estimator has the lowest runtime and DOA MSE comparing to the other well-known MC algorithms.