Finite sample performance of linear least squares estimators under sub-Gaussian martingale difference noise

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required. Surprisingly, bounding the probability of large errors with finitely many samples has been left open, especially when dealing with correlated noise with unknown covariance. In this paper we analyze the finite sample performance of the linear least squares estimator under sub-Gaussian martingale difference noise. In order to analyze this important question we used concentration of measure bounds. When applying these bounds we obtained tight bounds on the tail of the estimator's distribution. We show the fast exponential convergence of the number of samples required to ensure a given accuracy with high probability. We provide probability tail bounds on the estimation error's norm. Our analysis method is simple and uses simple $L_{\infty}$ type bounds on the estimation error. The tightness of the bounds is tested through simulation. The proposed bounds make it possible to predict the number of samples required for least squares estimation even when least squares is sub-optimal and used for computational simplicity. The finite sample analysis of least squares models with this general noise model is novel

Set Down Study of Projectile in Flight Through Imaging

Deformation study of projectile immediately after firing is essential for its successful impact. A projectile that undergoes more than the tolerated amount of deformation in the barrel may not produce the requisite results. The study of projectile deformation before its impact requires it to be imaged in flight and perform some computation on the acquired image. Often the deformation tolerance is of the order of tens of micrometer and the acquired image cannot produce image with such accuracy because of photographic limitations. Therefore, it demands sub-pixel manipulation of the captured projectile image. In this work the diameter of a projectile is estimated from its image which became blur because of slow shutter speed. First the blurred image is restored and then various interpolation methods are used for sub-pixel measurement. Two adaptive geometrical texture based interpolation schemes are also proposed in this research. The proposed methods produce very good results as compared to the existing methods.Science Journal, Vol. 64, No. 6, November 2014, pp.530-535, DOI:http://dx.doi.org/10.14429/dsj.64.811

Kinect Depth Recovery via the Cooperative Profit Random Forest Algorithm

The depth map captured by Kinect usually contain missing depth data. In this paper, we propose a novel method to recover the missing depth data with the guidance of depth information of each neighborhood pixel. In the proposed framework, a self-taught mechanism and a cooperative profit random forest (CPRF) algorithm are combined to predict the missing depth data based on the existing depth data and the corresponding RGB image. The proposed method can overcome the defects of the traditional methods which is prone to producing artifact or blur on the edge of objects. The experimental results on the Berkeley 3-D Object Dataset (B3DO) and the Middlebury benchmark dataset show that the proposed method outperforms the existing method for the recovery of the missing depth data. In particular, it has a good effect on maintaining the geometry of objects