A Novel Cascaded Image Transform by Varying Energy Density to Convert an Image in to Sparse

Background: All natural signals are subjected to sparsity when they are properly represented by a basis function. Sparsity helps us to sample the signals less than Nyquist rate which clearly explained by the recent theory known as compressive sensing. Methods: This paper explains that DFT does a good job in converting the given image into sparse when the energy density of the image is varied and also a cascaded transform DFT and DWT is proposed. Qualitative measures for the cascaded transform were observed to be good. Result: It helps us to convert a given image signal into sparse without loss in information content present in that image. Application: While converting an analog signal into digital, sparsity will help to compress a given analog signal before conversion. So the number of samples obtained by sampling the compressed signal becomes less.