Effective Image Reconstruction Using Various Compressed Sensing Techniques

The prevailing information relies heavily on the principles articulated by Shannon and Nyquist. These theories assert that, to faithfully reconstruct a signal without distortion, the sampling frequency must exceed twice the signal's maximum frequency to prevent aliasing. Following this, signals undergo compression to eliminate inherent redundancies before transmission over the channel. Despite the effectiveness of this approach, a significant drawback arises from the substantial processing overhead involved in sampling and compression. This limitation renders the scheme unsuitable for contemporary applications, given the constraints of current computational capabilities. Compressive Sensing (CS) introduces a novel framework, grounded in signal decomposition and approximation theory. Serving as an alternative to the Nyquist criteria, CS presents advantages such as reduced sensing time and sampling rate. In this approach, signals are sampled below the Nyquist rate through linear projection onto a random basis, ensuring exact reconstruction of the original signal. CS contributes to the reduction of power consumption and computational complexity in handling digital data. The extraction of information is facilitated by the utilization of a sensing matrix. In the context of image restoration, the CS framework provides an innovative approach to recover high-quality images from their compressed measurements. The success of image restoration in compressive sensing relies on the development of robust algorithms that can efficiently exploit sparsity while addressing the inherent tradeoff between accuracy and computational complexity. We survey state-of-the-art reconstruction algorithms, including iterative methods, convex optimization, and deep learning approaches, showcasing their strengths and limitations in restoring images from compressed measurements. The success of image restoration in compressive sensing relies on the development of robust algorithms that can efficiently exploit sparsity while addressing the inherent tradeoff between accuracy and computational complexity. We survey state-of-the-art reconstruction algorithms, including iterative methods, convex optimization, and deep learning approaches, showcasing their strengths and limitations in restoring images from compressed measurements.