Deterministic Way of Designing Sensing Matrix

With all the scientific and technological advancements, signal reconstruction is still a challenging problem in many ways. Mathematically, signal reconstruction is a linear map from the Hilbert space of square-integrable function LP to complex space Cn. We assume there can be any sampling method and a reconstruction formula for such a linear map. In principle, it is possible first to choose a reconstruction formula and then either compute some sampling algorithm based on the chosen reconstruction formula or analyse the behaviour of a given sampling algorithm concerning the given formula. In 1948, Claude Shannon's groundwork on the sampling theorem was published, which became the backbone for almost all types of digital signal processing techniques. This famous Nyquist – Shannon Sampling theorem follows a strict sufficient condition for the perfect reconstruction of the sampled signal. In 2004, the concept of compressive sensing was introduced, which uses the given knowledge of sparsity and can reconstruct the signal perfectly even with fewer samples compared to the samples required according to the sampling theorem. In compressive sensing, one measure of difficulty is designing the sensing matrix. Random matrices with Gaussian, Bernoulli, and Fourier entries are highly used as sensing matrices in compressive sensing for signal recovery. However, random matrices are not suitable for every application. In this paper, we provide a new deterministic way of designing a sensing matrix, provided we incorporate prior knowledge about signal acquisition. At the last, we will show the reconstruction result by using the proposed sensing matrix.