Method and device for perfectly incoherent sampling to a Haar domain

A non-transitory computer readable article of manufacture tangibly embodying computer readable instructions which when executed causes a computer to carry out the steps of a method for converting a signal, comprising steps of:

• applying a transform including a Haar transform and a Hadamard transform to a first representation of the signal in a first domain;
• and
• converting said first representation of the signal into a second representation of the signal in a second domain such that a basis of the second domain is maximally incoherent to a Haar basis;
• wherein at the step of applying, the Haar transform and the Hadamard transform are combined into n computational stages (P/Q1, P/Q2, P/Q3), wherein the jth computational stage takes outputs of a j−1th computational stage as input;
• and
• wherein the n computational stages (P/Q1, P/Q2, P/Q3) are each defined by:
• one or more stage-to-stage functions (P1, P2, P3);
• and one or more feed forward functions (Q1, Q2, Q3), wherein a stage-to-stage function for stage n is given by:
• P
• n
• =
• [
• I
• n
• -
• 1
• I
• n
• -
• 1
• I
• n
• -
• 1
• -
• I
• n
• -
• 1
• ]
• and wherein a feed forward function for stage n is given by:
• Q
• n
• =
• [
• E
• n
• -
• 1
• -
• E
• n
• -
• 1
• -
• E
• n
• -
• 1
• 3
• ⁢
• E
• n
• -
• 1
• ]
• ,
• with In being a 2n×2n identity matrix and En being a 2n×2n matrix consisting of 1's only, each of the feed forward functions and the stage-to-stage functions taking 2n elements of an input vector as input.