  Herein, security of deep neural network against adversarial attack is
considered. Existing compressive sensing based defence schemes assume that
adversarial perturbations are usually on high frequency components, whereas
recently it has been shown that low frequency perturbations are more effective.
This paper proposes a novel Compressive sensing based Adaptive Defence (CAD)
algorithm which combats distortion in frequency domain instead of time domain.
Unlike existing literature, the proposed CAD algorithm does not use information
about the type of attack such as l0, l2, l-infinity etc. CAD algorithm uses
exponential weight algorithm for exploration and exploitation to identify the
type of attack, compressive sampling matching pursuit (CoSaMP) to recover the
coefficients in spectral domain, and modified basis pursuit using a novel
constraint for l0, l-infinity norm attack. Tight performance bounds for various
recovery schemes meant for various attack types are also provided. Experimental
results against five state-of-the-art white box attacks on MNIST and CIFAR-10
show that the proposed CAD algorithm achieves excellent classification accuracy
and generates good quality reconstructed image with much lower computation
