Single Pixel Camera Using Compressed Sensing

The Single Pixel Camera is a setup that uses the compressed sensing algorithm to reconstruct an image from a sparse matrix. In today’s world, Data Acquisition and Data Storage are the two most important aspects of technology. The world is forever evolving, and so are the Data Acquisition mechanisms. On an average, an information of about 2 Giga Bytes is stored every second. This accounts for smart and effective data storage techniques. The pace at which the Data Storage needs are increasing is unfathomable. There is hardly any room for error and unrequired data. For this a method is needed that eliminates the unwanted data, keeping the useful data intact, distortion free. One such technique is Compressed Sensing. Compressed sensing is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Shannon-Nyquist sampling theorem. There are two conditions under which recovery is possible. The first one is sparsitywhich requires the signal to be sparse in some domain. The second one is incoherence which is applied through the isometric property which is sufficient for sparse signal. By using compressed sensing, one can obtain Super Resolved signals from just a few sensors. The sensing here is Non-Adaptive, no effort is done to understand the signal at circuit level, this makes it a faster approach when compared to its counter parts. The Sample Acquisition process is followed by numerical optimization. The Old Conventional Approach of image acquisition follows the Nyquist Criteria of sampling a signal, and thus takes as many values as the number of pixels. This process leads to accumulation of lots of unwanted data. The image can be correctly reconstructed even without this “Extra Data”. The Modern Approach, uses the concept of Sparse Matrix. A wavelet transform of the Image Matrix is taken, then a high proportion of values with less significance are zeroed. For Ex. In a matrix of 100,000 elements, every element except some 25000 elements is set to zeroes. The Setup for Single Pixel Camera includes a Photo detector, A DMD array (An Illuminated Screen can replace it.), Analog-To-Digital converter (ADC), A Computer for further optimization. The DMD array is used to display a random pattern of white and black blocks, due to which the intensity of light keeps on changing randomly with every new pattern. The Object is mirrored over this random pattern, and several readings are taken, with the pattern being different each time. The number of readings are very less, a few hundred when compared to that of several million readings of a normal camera.The reason this second method works stems from the idea that most natural images are sparse in bases ranging from cosines, wavelets to curvelets. Functions that represent random tilings of reflective and non-reflective mirrors (0s and 1s) are said to be mathematically "incoherent" with these bases thereby allowing an automatic compression at the detector levels. The project uses MATLAB as the major programming language.