Signal classification using sparse representation

1. A system comprising:

a processor for classifying an input signal, and

memory for storing data, wherein the processor is configured to:

receive the input signal for classification and a set of pre-classified signals, wherein the input signal and each signal in the set of pre-classified signals comprises a vector representation of an object having a plurality of vector elements;

determine a sparse vector comprising a plurality of sparse vector coefficients, each sparse vector coefficient corresponding to a signal in the set of pre-classified signals and representing a likelihood of a match between the object represented in the input signal and the object represented in the corresponding signal of the set of pre-classified signals, and

compare a largest sparse vector coefficient of the determined sparse vector with a predetermined threshold;

wherein, if the largest sparse vector coefficient is less than the predetermined threshold, the processor is further configured to:

remove the signal of the set of pre-classified signals corresponding to the largest sparse vector coefficient from the set of pre-classified signals to produce a reduced set of pre-classified signals, and

repeat, iteratively, the determining and comparing using the input signal and the reduced set of pre-classified signals, wherein, each iteration of the input signal includes

determining whether there has been a previous iteration for the input signal;

determining whether the largest sparse vector coefficient in a current iteration is less than the largest sparse vector coefficient in a previous iteration for the input signal, if there has been a previous iteration for the input signal, and

providing a classification output based on the signal of the set of pre-classified signals corresponding to the largest sparse vector coefficient in the previous iteration, if the largest sparse vector coefficient in the current iteration is less than the largest sparse vector coefficient in a previous iteration.

2. The system of claim 1 , wherein, prior to repeating the determining and comparing using the input signal and the reduced set of pre-classified signals, the processor is further configured to:

store the largest sparse vector coefficient in memory.

3. The system of claim 1 , wherein the processor is further configured to:

repeat the determining and comparing using the input signal and the reduced set of pre-classified signals until the largest sparse vector coefficient is greater than the predetermined threshold or the largest sparse vector coefficient in a current iteration for the input signal is less than the largest sparse vector coefficient in a previous iteration for the input signal.

4. The system of claim 1 , wherein the processor is further configured to:

perform a further iteration for the input signal, if there has not been a previous iteration for the input signal or if the largest sparse vector coefficient in the current iteration is greater than or equal to the largest sparse vector coefficient in a previous iteration.

5. The system of claim 1 , wherein the processor is further configured to:

determine the sparse vector by solving an optimization problem:

Ax=b

subject to x being as sparse as possible

wherein: A is an m×n matrix comprising n column vectors of m vector elements, each column vector corresponding to a vector representation of one of the pre-classified signals;

vector b is a column vector of m vector elements corresponding to the vector representation of the input signal, and

vector x is row vector of n vector elements, each corresponding to a sparse representation coefficient of the sparse vector solution.

6. The system of claim 5 , wherein if the largest sparse vector coefficient is greater than the predetermined threshold, the processor is configured to:

provide a classification output based on the signal of the set of pre-classified signals corresponding to the largest sparse vector coefficient.

7. The system of claim 1 , wherein the processor is further configured to determine a value of the predetermined threshold.

8. The system of claim 7 , wherein the processor is further configured to:

receive a plurality of input signals for classification and a set of pre-classified signals, wherein each of the plurality of input signals and each signal in the set of pre-classified signals comprises a vector representation of an object having a plurality of vector elements, and wherein the classification of each of the plurality of input signals is known; and

for each input signal:

determine a sparse vector comprising a plurality of sparse vector coefficients, each sparse vector coefficient corresponding to a signal in the set of pre-classified signals and representing a likelihood of a match between the object represented in the input signal and the object represented in the corresponding signal of the set of pre-classified signals;

determine whether the object represented in the pre-classified signal corresponding to the largest sparse vector coefficient of the determined sparse vector matches the object represented in the input signal;

store the value of the largest sparse vector coefficient in memory, wherein the value of the largest spare vector coefficient is stored in a first group of training data, if the object represented in the pre-classified signal corresponding thereto matches the object represented in the input signal, and in a second group of training data, if the object represented in the pre-classified signal corresponding thereto does not match the object represented in the input signal; and

determine a threshold value for the largest sparse vector coefficient based on the values stored in the first and second groups of training data in memory, wherein the threshold value represents a minimum value for the largest sparse vector coefficient indicative of a true positive match.

9. The system of claim 8 , wherein, prior to determining a threshold value, the processor is configured to:

determine whether the first and second groups of training data satisfy a minimum sample size for a statistically meaningful determination of the threshold value, and

obtain further training data using further input signals until the first and second groups of training data satisfy the minimum sample size, if the first and second groups of training data do not satisfy the minimum sample size.