On Selection of Search Space Dimension in Compressive Sampling Matching Pursuit

Compressive Sampling Matching Pursuit (CoSaMP) is one of the popular greedy methods in the emerging field of Compressed Sensing (CS). In addition to the appealing empirical performance, CoSaMP has also splendid theoretical guarantees for convergence. In this paper, we propose a modification in CoSaMP to adaptively choose the dimension of search space in each iteration, using a threshold based approach. Using Monte Carlo simulations, we show that this modification improves the reconstruction capability of the CoSaMP algorithm in clean as well as noisy measurement cases. From empirical observations, we also propose an optimum value for the threshold to use in applications.

Relook into the historical progress and philosophy of Indian space exploration

A study of the history and philosophy of the contribution of India towards the exploration of space since antiquity provides interesting insights. The contributions are described during the three periods namely: (1) the ten millenniums from 10,000 BC with a twilight period up to 900 AD; (2) the ten centuries from 900 AD to 1900 AD; and (3) the ten decades from 1900 AD to 2000 AD; called mythological, medieval, and modern respectively. Some important events during the above periods provide a reference view of the progress. The Vedas during the mythological period and the Siddhantas during the medieval periods, which are based on astronomical observations, indicate that the Indian contribution preceded other cultures. But most Western historians ignore this fact time and again in spite of many proofs provided to the contrary. This chapter also shows that Indians had the proper scientific attitude of developing any physical theory through the triplet of mind, model, and measurements. It is this same triplet that forms the basis of the present day well known Kalman filter technique. Up to about 1500 BC the Indian contribution was leading but during foreign invasion and occupation it lagged and has been improving only after independence.

Adaptive selection of search space in look ahead orthogonal matching pursuit

Compressive Sensing theory combines the signal sampling and compression for sparse signals resulting in reduction in sampling rate and computational complexity of the measurement system. In recent years, many recovery algorithms were proposed to reconstruct the signal efficiently. Look Ahead OMP (LAOMP) is a recently proposed method which uses a look ahead strategy and performs significantly better than other greedy methods. In this paper, we propose a modification to the LAOMP algorithm to choose the look ahead parameter L adaptively, thus reducing the complexity of the algorithm, without compromising on the performance. The performance of the algorithm is evaluated through Monte Carlo simulations.