• Utsav Bhatt
• Kishor Bamniya

This paper gives the conventional approach of reconstructing signals or images from calculated data by following the well-known Shannon sampling theorem. This principle underlies the majority devices of current technology, such as analog-to-digital conversion, medical imaging, or audio and video electronics. The primary objective of this paper is to establish the need of compressive sensing in the field of signal processing and image processing. Compressive sensing (CS) is a novel kind of sampling theory, which predicts that sparse signals and images can be reconstructed from what was in the past thought to be partial information. CS has two distinct major approaches to sparse recovery that each present different benefits and shortcomings. The first, ℓ1-minimization methods such as Basis Pursuit use a linear optimization problem to recover the signal. This method provides strong guarantees and stability, but relies on Linear Programming, whose methods do not yet have strong polynomially bounded run times. The second approach uses greedy methods that compute the support of the signal iteratively. These methods are much faster than Basis Pursuit, but until recently had not been able to provide the same guarantees. This gap between the two approaches was bridged when we developed and analyzed the greedy algorithm.

ℓ1-Minimization, Basic Pursuit, Greedy Algorithm, Shannon Sampling Theorem, Sparse, Incoherence.

"A Study on Compressive Sensing and Reconstruction Approach", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.2, Issue 5, page no.1630-1634, May-2015, Available :http://www.jetir.org/papers/JETIR1505053.pdf

"A Study on Compressive Sensing and Reconstruction Approach", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.2, Issue 5, page no. pp1630-1634, May-2015, Available at : http://www.jetir.org/papers/JETIR1505053.pdf