Description

Abstract: The number of coefficients of multidimensional (MD) finite-extent impulse response (FIR) filters increases exponentially with the number of dimensions leading to significantly high computational complexities. The M-D FIR filters having sparse impulse responses reduce the computational complexity significantly. Here, we first present a design method for M-D FIR filters having sparse coefficients, where we consider the design of M-D FIR filters with arbitrary frequency responses and low group delays of which the coefficients are complex valued. We then present example filter designs applied to beamforming of wideband signals received by a uniform linear array and volumetric refocusing of light fields where more than 60% reduction of computational complexity is achieved. We finally present the extension of the M-D sparse FIR filter design concept to design diffractive deep neural networks. We consider the application of a quantitative phase imaging microscope and show that diffractive layers with substantially sparse coefficients can be achieved.